On a conjecture concerning the Bruhat order

Rosário Fernandes, Henrique da Cruz, Domingos Salomão

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
7 Downloads (Pure)


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) ”.
Original languageEnglish
Pages (from-to)82-95
JournalLinear Algebra and its Applications
Publication statusPublished - 2020


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