Sign-restricted matrices of $0$'s, $1$'s, and $-1$'s
| Autor: | Geir Dahl, Richard A. Brualdi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Class (set theory) Algebra and Number Theory 010102 general mathematics Distributive lattice Polytope 010103 numerical & computational mathematics 01 natural sciences Column (database) Bruhat order Combinatorics 05A18 05B20 06A07 15B35 15B36 FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Combinatorics (math.CO) Geometry and Topology 0101 mathematics Sign (mathematics) Mathematics |
| ISSN: | 0024-3795 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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