Abstract
Given two nonincreasing integral vectors R and S, with the same sum, we denote by \(\mathcal {A}(R,S)\) the class of all (0,1)-matrices with row sum vector R, and column sum vector S. The Bruhat order and the Secondary Bruhat order on \(\mathcal {A}(R,S)\) are both extensions of the classical Bruhat order on Sn, the symmetric group of degree n. These two partial orders on \(\mathcal {A}(R,S)\) are, in general, different. In this paper we prove that if R = (2,2,…,2) or R = (1,1,…,1), then the Bruhat order and the Secondary Bruhat order on \(\mathcal {A}(R,S)\) coincide.
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Research partially supported by the projects UID/MAT/00297/2019, and UID/MAT/00212/2019.
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Fernandes, R., da Cruz, H.F. & Salomão, D. Classes of (0,1)-matrices Where the Bruhat Order and the Secondary Bruhat Order Coincide. Order 37, 207–221 (2020). https://doi.org/10.1007/s11083-019-09500-8
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DOI: https://doi.org/10.1007/s11083-019-09500-8