Sign-restricted matrices of 0's, 1's, and −1's.

We study 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. [ABSTRACT FROM AUTHOR]