Séminaire Lotharingien de Combinatoire, 93B.124 (2025), 12 pp.

Mark Skandera and Daniel Soskin

Multiplicative Permanental Inequalities for Totally Positive Matrices

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

Received: November 15, 2024. Accepted: February 15, 2025. Final version: April 1, 2025.

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