Sui q-archi completi di un piano non desarguesiano di ordine q pari
Abstract
A classic theorem by B. Segre [4], and G. Tallini, [6], states that in a finite desarguesian plane of order q no complete q-arc exists. This result can not be extended to any non desarguesian plane ([1],[2],[3]).
In this paper we consider a non desarguesian plane πq of even order q greater or equal to 16 and we study complete q-arcs admitting one point of index q-4 in πq. As it is well known, [5], the admissible values for the index of the remaining points of πq are 0,2,4,6,8. We prove that the non existence of any point of index 8 implies q lesser or equal to 34.
Downloads
Published
Issue
Section
License
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).
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.
No Fee Charging
No fee is required to complete the submission/review/publishing process of authors paper.
