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arXiv · 2101.04150

Sign-restricted matrices of $0$'s, $1$'s, and $-1$'s

Richard A. Brualdi·Geir Dahl
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Abstract

We study {\em sign-restricted matrices} (SRMs), a class of rectangular $(0, \pm 1)$-matrices generalizing the alternating sign matrices (ASMs). In an SRM each partial column sum, starting from row 1, equals 0 or 1, and each partial row sum, starting from column 1, is nonnegative. We determine the maximum number of nonzeros in SRMs and characterize the possible row and column sum vectors. Moreover, a number of results on interchange operations are shown, both for SRMs and, more generally, for $(0, \pm 1)$-matrices. The Bruhat order on ASMs can be extended to SRMs with the result a distributive lattice. Also, we study polytopes associated with SRMs and some relates decompositions.

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Richard A. Brualdi, Geir Dahl. 2021-01-11. Sign-restricted matrices of $0$'s, $1$'s, and $-1$'s. https://arxiv.org/abs/2101.04150

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