A combinatorial generalization of the Durfee square
The Durfee square of a partition λ, D(λ), is defined as the largest square contained in the shape of λ.
It was proved in  (cf. also ) that the size of D(λ), d(λ), was related to the perfection of a certain module M_λ , an algebro-geometric object (cf. also , , ). The goal of this note is to propose a generalization of the notion of Durfee square to the case of a pair (α, β) of partitions.
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