Parametrizations of k-nonnegative matrices: Cluster algebras and k-positivity tests

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:174

Article

关键词: Totally positive matrices;    k-Nonnegative matrices;    Cluster algebras;    Double wiring diagrams;   

DOI  :  10.1016/j.jcta.2020.105217

来源: Elsevier

【 摘 要 】

A k-positive matrix is a matrix where all minors of order k or less are positive. Computing all such minors to test for k-positivity is inefficient, as there are Sigma(k)(l=1) ((n)(l))(2) of them in an n x n matrix. However, there are minimal k-positivity tests which only require testing n(2) minors. These minimal tests can be related by series of exchanges, and form a family of sub-cluster algebras of the cluster algebra of total positivity tests. We give a description of the sub-cluster algebras that give k-positivity tests, ways to move between them, and an alternative combinatorial description of many of the tests. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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