2021/01/11 by Brualdi, Richard A., Dahl, Geir
#05A18 #05B20 #06A07 #15B35 #15B36 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2101.04150
We study \em sign-restricted matrices (SRMs), a class of rectangular (0, ± 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, ± 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.