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

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