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On a conjecture concerning the Bruhat order
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Orientador(es)
Resumo(s)
Let R and S be two sequences of positive integers in nonincreasing order having the same sum. Let A(R,S) be the class of all (0,1)-matrices with row sum vector R and column sum vector S. If A(R,S) is nonempty, an inversion in AεA(R,S) consists of two entries of A equal to 1, one of them is located to the top-right of the other. Let γ(A) be the total number of inversions in A. The Bruhat order is a partial order defined on A(R,S) and denoted by ≤ . In this paper, we prove the conjecture: “If A,CεA(R,S), A≠C and A≤C then γ(A)<γ(C) ”.
Descrição
partially supported by the Fundacao para a Ciencia e a Tecnologia through the project UIBD/MAT/00297/2020. project UID/MAT/00212/2019.