Le Matematiche
type: channel
description: Journal of Pure and Applied Mathematics and Information Science Open Access Journal
publisher: Dipartimento di Matematica e Informatica
language: en
publication name: Le Matematiche
issn: 0373-3505
copyright: The authors retain all rights to the original work without any restrictions. License for Published Contents "Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Licence scheme | Legal code License for Metadata "Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. Licence scheme | Legal code No Fee Charging No fee is required to complete the submission/review/publishing process of authors paper.
items: On semi-c-periodic functions of type I and applications
items: Elastic beam qquations with variable coefficients: multiple solutions under mixed nonlinearities
items: What is Positive Geometry?
items: Nonnil-Noetherian pairs of the form (R, R[X]) and some related results
items: Local and global solvability in attraction-repulsion chemotaxis systems with L2-initial data
items: On all-path convex, gated and Chebyshev sets in graphs
items: Moduli spaces in positive geometry
items: The two-loop amplituhedron
items: The positive orthogonal grassmannian
items: Points on rational normal curves and the ABCT variety
items: Cyclic polylopes through the lense of iterated integrals
items: Tropicalizing binary geometries
items: Uniqueness of MHV gravity amplitudes
items: The chirotropical grassmannian
items: Proudfoot-Speyer degenerations of scattering equations
items: Logarithmic discriminants of hyperplane arrangements
items: Binary geometries from pellytopes
items: Differential equations for moving hyperplane arrangements
items: Algebraic approaches to cosmological integrals
items: Multiple solutions for a dynamic Sturm-Liouville boundary value problem on time scales with impulsive effects
items: From Feynman diagrams to the amplituhedron: a gentle review
items: How to stab a polytope
items: Kinematic varieties for massless particles
items: Hyperplane arrangements in the grassmannian
items: Chow-Lam recovery
items: An explicit lower bound for large gaps between some consecutive primes
items: Bivariate exponential integrals and edge-bicolored graphs
items: Sign-changing solutions for a nonlinear degenerate elliptic system
items: Global solvability of the Laplace equation in weighted Sobolev spaces
items: Construction of 3-helix systems of any index

On semi-c-periodic functions of type I and applications
type: item
description: In this paper, we study the (newly introduced) class of functions called semi-c-periodic functions of type I in a Banach space. We first investigate their basic properties, including a convolution result. Using a suitable norm we prove that the set of such functions is a Banach space. We then study the existence and uniqueness of semi-c-periodic mild solutions for both autonomous and non-autonomous linear evolution equations. We achieve the existence results using the Banach fixed point theorem and the principle of reduction
subject: Articoli
  topic: section
subject: C-periodic; Semi-c-periodic; Uniformly close c-periodic; Volterra integral equation; Banach fixed point principle
  topic: keywords
creator: Ruwaida Aldrsoni
creator: Gaston N'Guerekata
rights: Copyright (c) 2025 R. Aldrsoni, G. N'Guerekata http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 771
ending page: 789

Elastic beam qquations with variable coefficients: multiple solutions under mixed nonlinearities
type: item
description: This paper investigates the existence of multiple solutions for a fourth-order differential equation modelling an elastic beam, where the coefficients are variable, and the nonlinearities exhibit both concave and convex characteristics. Our approach is based on variational methods and critical point theorems, particularly those formulated by Ricceri, which provide a powerful framework for proving the existence of solutions in reflexive Banach spaces. By leveraging these mathematical tools, we establish that the considered problem admits at least three distinct weak solutions under specific conditions. To validate our theoretical findings, we present an illustrative example demonstrating how our results can be applied in practice.
subject: Articoli
  topic: section
creator: Shapour Heidarkhani
creator: Shahin Moradi
creator: Anderson L. A. De Araujo
creator: David Barilla
rights: Copyright (c) 2025 S. Heidarkhani, S. Moradi, A. L. A. De Araujo, D. Barilla http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 749
ending page: 769

What is Positive Geometry?
type: item
description: This article serves as an introduction to the special volume on Positive Geometry in the journal Le Matematiche. We attempt to answer the question in the title by describing the origins and objects of positive geometry at this early stage of its development. We discuss the problems addressed in the volume and report on the progress. We also list some open challenges.
subject: Articoli
  topic: section
subject: Positive Geometry
  topic: keywords
creator: K. Ranestad
creator: B. Sturmfels
creator: S. Telen
rights: Copyright (c) 2025 K. Ranestad, B. Sturmfels, S. Telen http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 3
ending page: 16

Nonnil-Noetherian pairs of the form (R, R[X]) and some related results
type: item
description: The rings considered in this paper are commutative with identity and are nonzero. Let R be a ring. An ideal I of R is said to be nonnil if it is not contained in the nilradical of R. We say that R is nonnil-Noetherian (resp., nonnil-Laskerian) if each proper nonnil ideal of R is finitely generated (resp., admits a primary decomposition). Whenever T is an extension ring of R, we assume that R contains the identity element of T. Let T be an extension ring of R. We say that (R, T) is a Nonnil-Noetherian pair (resp., Nonnil-Laskerian pair) if f A is nonnil-Noetherian (resp., nonnil-Laskerian) for any intermediate ring A between R and T. This paper aims to characterize R such that (R, R[X]) is a nonnil-Noetherian pair (resp., nonnil-Laskerian pair), where R[X] is the polynomial ring in one variable X over R. Also, this paper aims to characterize R such that each intermediate ring A between R and R[X] posses a property which is related to being nonnil-Noetherian (resp., nonnil-Laskerian).
subject: Articoli
  topic: section
creator: S. Visweswaran
rights: Copyright (c) 2025 S. Visweswaran http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 729
ending page: 747

Local and global solvability in attraction-repulsion chemotaxis systems with L2-initial data
type: item
description: This paper deals with the attraction-repulsion chemotaxis system under homogeneous Neumann initial-boundary conditions, where Ω ⊂ Rn (n ≤ 3) is a smoothly bounded domain and a,b,c,χ,ξ,α,β,γ,δ > 0 and τ ∈ {0, 1} are constants. The purpose of the present paper is to construct a local solution of this system for any L2-initial data without additional conditions on χ and ξ by using the theory for abstract evolution equations and to extend the local solution globally in the repulsion-dominant case by relying on a priori estimates.
subject: Articoli
  topic: section
subject: abstract evolution equations
  topic: keywords
subject: $L^2$-initial data
  topic: keywords
subject: local existence
  topic: keywords
subject: attraction-repulsion chemotaxis systems
  topic: keywords
creator: Yutaro Chiyo
creator: Taisho Saga
creator: Tomomi Yokota
rights: Copyright (c) 2025 Y. Chiyo, T. Saga, T. Yokota http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 701
ending page: 727

On all-path convex, gated and Chebyshev sets in graphs
type: item
description: We present new characterizations for trees, block graphs, and geodetic graphs using all-path convex, gated and Chebyshev sets. Specifically, we prove that trees are exactly the graphs in which all-path convexity is a convex geometry. Block graphs are characterized as graphs in which all balls are all-path convex (equivalently, gated), and geodetic graphs are exactly those graphs where all balls (equivalently, closed neighborhoods) are Chebyshev. Additionally, we prove that almost all graphs have geodesically convex Chebyshev sets, provide a characterization of bipartite graphs with connected Chebyshev sets, and establish a criterion for graphs with trivial Chebyshev sets in the class of graph joins. Finally, we show that graphs of odd order with maximal number of edges under the Seidel switching operation always have trivial Chebyshev sets.
subject: Articoli
  topic: section
subject: all-path convexity
  topic: keywords
subject: geodesic convexity
  topic: keywords
subject: gated set
  topic: keywords
subject: Chebyshev set
  topic: keywords
subject: block graph
  topic: keywords
subject: tree
  topic: keywords
creator: Vladyslav Haponenko
creator: Sergiy Kozerenko
rights: Copyright (c) 2025 V. Haponenko, S. Kozerenko http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 661
ending page: 678

Moduli spaces in positive geometry
type: item
description: These are lecture notes for five lectures given at MPI Leipzig in May 2024. We study the moduli space M0,n of n distinct points on P1 as a positive geometry and a binary geometry. We develop mathematical formalism to study Cachazo-He-Yuan's scattering equations and the associated scalar and Yang-Mills amplitudes. We discuss open superstring amplitudes and relations to tropical geometry.
subject: Articoli
  topic: section
creator: T. Lam
rights: Copyright (c) 2025 T. Lam http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 17
ending page: 101

The two-loop amplituhedron
type: item
description: The loop-Amplituhedron A(L)n is a semialgebraic set in the product of Grassmannians GrR(2,4)L. Recently, many aspects of this geometry for the case of L=1 have been elucidated, such as its algebraic and face stratification, its residual arrangement and the existence and uniqueness of the adjoint. This paper extends this analysis to the simplest higher loop case given by the two-loop four-point Amplituhedron A(2)4$.
subject: Articoli
  topic: section
subject: positive geometry
  topic: keywords
subject: Amplituhedron
  topic: keywords
subject: Amplitudes
  topic: keywords
creator: G. Dian
creator: E. Mazzucchelli
creator: F. Tellander
rights: Copyright (c) 2025 G. Dian, E. Mazzucchelli, F. Tellander http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 255
ending page: 277

The positive orthogonal grassmannian
type: item
description: The Plücker positive region OGr+(k,2k) of the orthogonal Grassmannian emerged as the positive geometry behind the ABJM scattering amplitudes. In this paper we initiate the study of the positive orthogonal Grassmannian OGr+(k,n) for general values of k, n. We determine the boundary structure of the quadric OGr+(1,n) in Pn-1+ and show that it is a positive geometry. We show that OGr+(k,2k+1) is isomorphic to OGr+(k+1, 2k+2) and connect its combinatorial structure to matchings on [2k+2]. Finally, we show that in the case n > 2k+1, the positroid cells of Gr+(k,n) do not induce a CW cell decomposition of OGr+(k,n).
subject: Articoli
  topic: section
subject: Orthogonal Grassmannian
  topic: keywords
subject: Flag variety
  topic: keywords
subject: Positive geometry
  topic: keywords
subject: Gröbner bases
  topic: keywords
subject: Straightening laws
  topic: keywords
creator: Y. El Maazouz
creator: Y. Mandelshtam
rights: Copyright (c) 2025 Y. El Maazouz, Y. Mandelshtam http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 279
ending page: 302

Points on rational normal curves and the ABCT variety
type: item
description: The ABCT variety is defined as the closure of the image of G(2, n) under the Veronese map. We realize the ABCT variety V(3,n) as the determinantal variety of a vector bundle morphism. We use this to give a recursive formula for the fundamental class of V(3,n). As an application, we show that special Schubert coefficients of this class are given by Eulerian numbers, matching a formula by Cachazo-He-Yuan. On the way tothis, we prove that the variety of configuration of points on a common divisor on a smooth variety is reduced and irreducible, generalizing a result of Caminata-Moon-Schaffler.
subject: Articoli
  topic: section
subject: rational normal curve, configurations, Grassmannian, positive geometry, spinor helicity, scattering equations
  topic: keywords
creator: D. Agostini
creator: L. Ramesh
creator: D. Shen
rights: Copyright (c) 2025 D. Agostini, L. Ramesh, D. Shen http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 103
ending page: 122

Cyclic polylopes through the lense of iterated integrals
type: item
description: The volume of a cyclic polytope can be obtained by forming an it- erated integral, known as the path signature, along a suitable piecewise linear path running through its edges. Different choices of such a path are related by the action of a subgroup of the combinatorial automorphisms of the polytope. Motivated by this observation, we look for other polyno- mials in the vertices of a cyclic polytope that arise as path signatures and are invariant under the subgroup action. We prove that there are infinitely many such invariants which are algebraically independent in the shuffle algebra.
subject: Articoli
  topic: section
subject: Piecewise linear paths
  topic: keywords
subject: Shuffle algebra
  topic: keywords
subject: Group action
  topic: keywords
subject: Signed volume
  topic: keywords
subject: Invariants
  topic: keywords
subject: Positive Matrices
  topic: keywords
creator: F. Lotter
creator: R. Preiß
rights: Copyright (c) 2025 F. Lotter, R. Preiß http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 365
ending page: 385

Tropicalizing binary geometries
type: item
description: The type A cluster configuration space, commonly known as M0,n, is the very affine part of the binary geometry associated with the associahedron. The tropicalization of M0,n can be realized as the space of phylogenetic trees and its signed tropicalizations as the dual-associahedron subfans. We give a concise overview of this construction and propose an extension to type C. The type C cluster configuration space MCl arises from the binary geometry associated with the cyclohedron. We define a space of axially symmetric phylogenetic trees containing many dual-associahedron and dual-cyclohedron subfans. We conjecturally realize the tropicalization of MCl as the defined space and its signed tropicalizations as the aforementioned subfans.
subject: Articoli
  topic: section
subject: tropical geometry
  topic: keywords
subject: cluster varieties
  topic: keywords
subject: phylogenetic trees
  topic: keywords
subject: associahedra
  topic: keywords
subject: binary geometries
  topic: keywords
creator: S. Cox
creator: I. Makhlin
rights: Copyright (c) 2025 S. Cox, I. Makhlin http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 211
ending page: 231

Uniqueness of MHV gravity amplitudes
type: item
description: We investigate MHV tree-level gravity amplitudes as defined on the spinor-helicity variety. Unlike their gluon counterparts, the gravity amplitudes do not have logarithmic singularities and do not admit Amplituhedron-like construction. Importantly, they are not determined just by their singularities, but rather their numerators have interesting zeroes. We make a conjecture about the uniqueness of the numerator and explore this feature from a more mathematical perspective. This leads us to a new approach for examining adjoints. We outline steps of our proposed proof and provide computational evidence for its validity in specific cases.
subject: Articoli
  topic: section
subject: scattering amplitudes, adjoints, commutative algebra
  topic: keywords
creator: J. Koefler
creator: U. Oktem
creator: S. Paranjape
creator: J. Trnka
creator: B. Zacovic
rights: Copyright (c) 2025 J. Koefler, U. Oktem, S. Paranjape, J. Trnka, B. Zacovic http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 347
ending page: 364

The chirotropical grassmannian
type: item
description: Recent developments in particle physics have revealed deep connections between scattering amplitudes and tropical geometry. From the heart of this relationship emerged the chirotropical Grassmannian TropχG(k,n) and the chirotropical Dressian Drχ(k,n), polyhedral fans built from uniform realizable chirotopes that encode the combinatorial structure of Generalized Feynman Diagrams. We prove that TropχG(3,n) = Drχ(3,n) for $n = 6,7,8$, and develop algorithms to compute these objects from their rays modulo lineality. Using these algorithms, we compute all chirotropical Grassmannians TropχG(3,n) for n = 6,7,8 across all isomorphism classes of chirotopes. We prove that each chirotopal configuration space Xχ(3,6) is diffeomorphic to a polytope and propose an associated canonical logarithmic differential form. Finally, we show that the equality between chirotropical Grassmannian and Dressian fails for (k,n) = (4,8).
subject: Articoli
  topic: section
subject: tropical geometry
  topic: keywords
subject: configuration space
  topic: keywords
subject: matroids
  topic: keywords
subject: scattering amplitudes
  topic: keywords
creator: D. Antolini
creator: N. Early
rights: Copyright (c) 2025 D. Antolini, N. Early http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 123
ending page: 142

Proudfoot-Speyer degenerations of scattering equations
type: item
description: We study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as linear equations on a reciprocal linear space and develop a degeneration-based homotopy algorithm for solving them. We investigate the Hilbert regularity of the corresponding homogeneous ideal and apply our methods to CHY scattering equations.
subject: Articoli
  topic: section
subject: hyperplane arrangements
  topic: keywords
subject: scattering equations
  topic: keywords
subject: maximum likelihood estimation
  topic: keywords
subject: homotopy continuation
  topic: keywords
subject: Hilbert regularity
  topic: keywords
creator: B. Betti
creator: V. Borovik
creator: S. Telen
rights: Copyright (c) 2025 B. Betti, V. Borovik, S. Telen http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 143
ending page: 165

Logarithmic discriminants of hyperplane arrangements
type: item
description: A recurring task in particle physics and statistics is to compute the complex critical points of a product of powers of affine-linear functions. The logarithmic discriminant characterizes exponents for which such a function has a degenerate critical point in the corresponding hyperplane arrangement complement. We study properties of this discriminant, exploiting its connection with the Hurwitz form of a reciprocal linear space.
subject: Articoli
  topic: section
subject: discriminant
  topic: keywords
subject: hyperplane arrangement
  topic: keywords
subject: scattering equations
  topic: keywords
subject: likelihood equations
  topic: keywords
creator: L. Kayser
creator: A. Kretschmer
creator: S. Telen
rights: Copyright (c) 2025 L. Kayser, A. Kretschmer, S. Telen http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 325
ending page: 346

Binary geometries from pellytopes
type: item
description: Binary geometries have recently been introduced in particle physics in connection with stringy integrals. In this work, we study a class of simple polytopes, called \emph{pellytopes}, whose number of vertices are given by Pell's numbers. We provide a new family of binary geometries determined by pellytopes as conjectured by He--Li--Raman--Zhang. We relate this family to the moduli space of curves by comparing the pellytope to the ABHY associahedron.
subject: Articoli
  topic: section
subject: binary geometry
  topic: keywords
subject: Pell's number
  topic: keywords
subject: moduli space of curves
  topic: keywords
creator: L. Bossinger
creator: M.L. Telek
creator: H. Tillmann-Morris
rights: Copyright (c) 2025 L. Bossinger, M.L. Telek, H. Tillmann-Morris http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 189
ending page: 209

Differential equations for moving hyperplane arrangements
type: item
description: We investigate Mellin integrals of products of hyperplanes, raised to an individual power each. We refer to the resulting functions as combinatorial correlators. We investigate their behavior when moving the hyperplanes individually. To encode these functions as holonomic functions in the constant terms of the hyperplanes, we aim to construct a holonomic annihilating D-ideal purely in terms of the hyperplane arrangement.
subject: Articoli
  topic: section
subject: Algebraic Analysis
  topic: keywords
subject: Holonomic Function
  topic: keywords
subject: Combinatorial Correlator
  topic: keywords
subject: Hyperplane Arrangement
  topic: keywords
creator: A. Pfister
creator: A.-L. Sattelberger
rights: Copyright (c) 2025 A. Pfister, A.-L. Sattelberger http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 409
ending page: 429

Algebraic approaches to cosmological integrals
type: item
description: Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space wavefunction. The singularities of these cosmological integrals are parameterized by binary hyperplane arrangements. Using different algebraic tools, we shed light on the differential and difference equations satisfied by these integrals. Moreover, we study a multivariate version of partial fractioning of the flat space wavefunction, and propose a graph-based algorithm to compute this decomposition.
subject: Articoli
  topic: section
subject: Cosmological correlators
  topic: keywords
subject: D-modules
  topic: keywords
subject: Wavefunction
  topic: keywords
subject: restricted GKZ systems
  topic: keywords
subject: multivariate partial fraction
  topic: keywords
creator: C. Fevola
creator: G. L. Pimentel
creator: A.-L. Sattelberger
creator: T. Westerdijk
rights: Copyright (c) 2025 C. Fevola, G. L. Pimentel, A.-L. Sattelberger , T. Westerdijk http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 303
ending page: 324

Multiple solutions for a dynamic Sturm-Liouville boundary value problem on time scales with impulsive effects
type: item
description: In this study, we explore the existence of multiple solutions for a dynamic Sturm-Liouville boundary value problem on time scales that incorporate impulsive effects. Utilizing variational methods and applying certain critical point theorems from Ricceri for smooth functionals, we demonstrate the existence of at least three solutions to the problem. To illustrate the practical relevance of our findings, we provide an example at the end.
subject: Articoli
  topic: section
creator: Massimiliano Ferrara
creator: Shapour Heidarkhani
creator: Shahin Moradi
creator: Anderson L.A. de Araujo
rights: Copyright (c) 2025 M. Ferrara, S. Heidarkhani, S. Moradi, A.L.A. de Araujo http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 679
ending page: 700

From Feynman diagrams to the amplituhedron: a gentle review
type: item
description: In this article we review, for a mathematical audience, the computation of (tree-level) scattering amplitudes in Yang-Mills theory in detail. In particular we demonstrate explicitly how the same formulas for six-particle NMHV helicity amplitudes are obtained from summing Feynman diagrams and from computing the canonical form of the n=6, k=1, m=4 amplituhedron.
subject: Articoli
  topic: section
subject: amplituhedron
  topic: keywords
subject: Feynman diagrams
  topic: keywords
subject: scattering amplitudes
  topic: keywords
creator: S. De
creator: D. Pavlov
creator: M. Spradlin
creator: A. Volovich
rights: Copyright (c) 2025 S. De, D. Pavlov, M. Spradlin, A. Volovich http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 233
ending page: 254

How to stab a polytope
type: item
description: We study the set of linear subspaces of a fixed dimension intersecting a given polytope. To describe this set as a semialgebraic subset of a Grassmannian, we introduce a Schubert arrangement of the polytope, defined by the Chow forms of the polytope’s faces of complementary dimension. We show that the set of subspaces intersecting a specified family of faces is defined by fixing the sign of the Chow forms of their boundaries. We give inequalities defining the set of stabbing subspaces in terms of sign conditions on the Chow form.
subject: Articoli
  topic: section
subject: Polytopes
  topic: keywords
subject: Grassmannian
  topic: keywords
subject: Combinatorial Geometry
  topic: keywords
subject: Schubert divisors
  topic: keywords
creator: S. Seemann
creator: F. Zaffalon
rights: Copyright (c) 2025 S. Seemann, F. Zaffalon http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 473
ending page: 493

Kinematic varieties for massless particles
type: item
description: We study algebraic varieties that encode the kinematic data for n massless particles in d-dimensional spacetime subject to momentum conservation. Their coordinates are spinor brackets, which we derive from the Clifford algebra associated to the Lorentz group. This was proposed for d=5 in the recent physics literature. Our kinematic varieties are given by polynomial constraints on tensors with both symmetric and skew symmetric slices.
subject: Articoli
  topic: section
subject: Spinor brackets
  topic: keywords
subject: Clifford algebra
  topic: keywords
subject: Grassmannian
  topic: keywords
subject: Determinantal Variety
  topic: keywords
subject: Tensor
  topic: keywords
creator: S. Rajan
creator: B. Sturmfels
creator: S. Sverrisdottir
rights: Copyright (c) 2025 S. Rajan, B. Sturmfels, S. Sverrisdottir http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 453
ending page: 471

Hyperplane arrangements in the grassmannian
type: item
description: The Euler characteristic of a smooth very affine variety encodes the algebraic complexity of solving likelihood (or scattering) equations on this variety. We study this quantity for the Grassmannian with d hyperplane sections removed. We provide a combinatorial formula, and explain how to compute this Euler characteristic in practice, both symbolically and numerically. Our particular focus is on generic hyperplane sections and on Schubert divisors. We also consider special Schubert arrangements relevant for physics. We study both the complex and the real case.
subject: Articoli
  topic: section
subject: Grassmannian
  topic: keywords
subject: Schubert divisors
  topic: keywords
subject: Euler characteristic
  topic: keywords
creator: E. Mazzucchelli
creator: D. Pavlov
creator: K. Wang
rights: Copyright (c) 2025 E. Mazzucchelli, D. Pavlov, K. Wang http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 387
ending page: 408

Chow-Lam recovery
type: item
description: We study the conditions under which a subvariety of the Grassmannian may be recovered from certain of its linear projections. In the special case that our Grassmannian is projective space, this is equivalent to asking when a variety can be recovered from its Chow form; the answer is "always" by work of Chow in 1937. In the general Grassmannian setting, the analogous question is when a variety can be recovered from its Chow-Lam form. We give both necessary conditions for recovery and families of examples where, in contrast with the projective case, recovery is not possible.
subject: Articoli
  topic: section
subject: positive geometry
  topic: keywords
subject: Chow form
  topic: keywords
creator: E. Pratt
creator: K. Ranestad
rights: Copyright (c) 2025 E. Pratt, K. Ranestad http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 431
ending page: 451

An explicit lower bound for large gaps between some consecutive primes
type: item
description: The main purpose of this paper is to clarify the numerical value of the constant cLG such that the above in- equality holds. We see that cLG is determined by several factors related to analytic number theory, for example, the ratio of integrals of functions in the multidimensional sieve of Maynard [14], the distribution of primes in arithmetic progressions to large moduli, and the coefficient of upper bound sieve of Selberg. We prove that the above inequality is valid at least for some cLG ≥ 2.0 × 10−17 .
subject: Articoli
  topic: section
creator: Keiju Sono
rights: Copyright (c) 2025 K. Sono http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 521
ending page: 544

Bivariate exponential integrals and edge-bicolored graphs
type: item
description: We show that specific exponential bivariate integrals serve as generating functions of labeled edge-bicolored graphs. Based on this, we prove an asymptotic formula for the number of regular edge-bicolored graphs with arbitrary weights assigned to different vertex incidence structures. The asymptotic behavior is governed by the critical points of a polynomial. As an application, we discuss the Ising model on a random 4-regular graph and show how its phase transitions arise from our formula.
subject: Articoli
  topic: section
subject: Edge-bicolored graphs
  topic: keywords
subject: Generating function
  topic: keywords
subject: Asymptotic behavior
  topic: keywords
subject: Bivariate exponential
  topic: keywords
subject: Critical points
  topic: keywords
creator: M. Borinsky
creator: C. Meroni
creator: M. Wiesmann
rights: Copyright (c) 2025 M. Borinsky, C. Meroni, M. Wiesmann http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 167
ending page: 187

Sign-changing solutions for a nonlinear degenerate elliptic system
type: item
description: In this article, we study the multiplicity of weak solutions to the non-linear degenerate elliptic system. The existence of sign-changing solutions is proved by the truncation method and the invariant sets of descending flow method.
subject: Articoli
  topic: section
subject: degenerate elliptic system
  topic: keywords
subject: truncation method
  topic: keywords
subject: sign-changing solutions
  topic: keywords
subject: method of invariant sets of descending flow
  topic: keywords
creator: Le Thi Hong Hanh
creator: Duong Trong
rights: Copyright (c) 2025 L. Thi Hong Hanh, D. Trong http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 641
ending page: 659

Global solvability of the Laplace equation in weighted Sobolev spaces
type: item
description: We consider a non-local boundary value problem for the Laplace equation in an unbounded strip, studying the weak and strong solvability of the problem within the framework of the weighted Sobolev space W1,pν with a Muckenhoupt weight. Utilising tools from non-harmonic analysis, we prove that any weak solution belonging to W2,pν is also a strong solution and satisfies the corresponding boundary conditions. It is worth noting that such problems do not fall within the scope of the general theory of elliptic equations and therefore require a specialized approach.
subject: Articoli
  topic: section
creator: Bilal Bilalov
creator: Natavan Nasibova
creator: Lyoubomira Softova
creator: Salvatore Tramontano
rights: Copyright (c) 2025 B. Bilalov, N. Nasibova, L. Softova, S. Tramontano http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 593
ending page: 612

Construction of 3-helix systems of any index
type: item
description: Let H(3) be a uniform of rank 3 hypergraph. A 3-helix S(3)(1,3) of \emph{centre} {c} is a 3-uniform hypergraph, with 3 hyperedges, all having in common exactly the centre {c}, with c of degree 3 and the remaining vertices of degree 1. In this paper we determine the spectrum of all S(3)(1,3)-designs, for every index λ.
subject: Articoli
  topic: section
creator: Antonio Causa
creator: Mario Gionfriddo
creator: Elena Maria Guardo
rights: Copyright (c) 2024 A. Causa, M. Gionfriddo, E.M. Guardo http://creativecommons.org/licenses/by/4.0
date: 2024-12-28
publication date: 2024-12-28
starting page: 469
ending page: 476