Sign-restricted matrices of $0$'s, $1$'s, and $-1$'s
Combinatorics
2021-01-13 v1
Abstract
We study {\em sign-restricted matrices} (SRMs), a class of rectangular -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 -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.
Keywords
Cite
@article{arxiv.2101.04150,
title = {Sign-restricted matrices of $0$'s, $1$'s, and $-1$'s},
author = {Richard A. Brualdi and Geir Dahl},
journal= {arXiv preprint arXiv:2101.04150},
year = {2021}
}