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- W2564871730 abstract "We introduce a new directed graph structure into the set of alternating sign matrices. This includes Bruhat graph (Bruhat order) of the symmetric groups as a subgraph (subposet). Drake–Gerrish–Skandera (2004, 2006) [6] , [7] gave characterizations of Bruhat order in terms of total nonnegativity (TNN) and subtraction-free Laurent (SFL) expressions for permutation monomials. With our directed graph, we extend their idea in two ways: first, from permutations to alternating sign matrices; second, q -analogs (which we name q TNN and q SFL properties). As a by-product, we obtain a new kind of permutation statistic, the signed bigrassmannian statistics, using Dodgson's condensation on determinants." @default.
- W2564871730 created "2017-01-06" @default.
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- W2564871730 date "2017-04-01" @default.
- W2564871730 modified "2023-09-29" @default.
- W2564871730 title "A directed graph structure of alternating sign matrices" @default.
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- W2564871730 doi "https://doi.org/10.1016/j.laa.2016.12.031" @default.
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