Permanental inequalities for totally positive matrices

2024/06/03 by Mark Skandera, Skandera, Mark, Daniel Soskin +1
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2406.00963

openalex publication_date 2024/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize ratios of permanents of (generalized) submatrices which are bounded on the set of all totally positive matrices. This provides a permanental analog of results of Fallat, Gekhtman, and Johnson [\em Adv. Appl. Math. \bf 30 no. 3, (2003) pp. 442--470] concerning ratios of matrix minors. We also extend work of Drake, Gerrish, and the first author [\em Electron. J. Combin., \bf 11 no. 1, (2004) Note 6] by characterizing the differences of monomials in ℤ[x_1,1,x_1,2,...,x_n,n] which evaluate positively on the set of all totally positive n × n matrices.

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