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 [Adv. Appl. Math. 30 (2003), 442-470] concerning ratios of matrix minors. We also extend work of Drake, Gerrish, and the first author [Electron. J. Combin. 11 (2004), #N6] by characterizing the differences of monomials in $\mathbb{Z}[x_{1,1},x_{1,2},\dotsc,x_{n,n}]$ which evaluate positively on the set of all totally positive $n \times n$ matrices.
@article{10_37236_13098,
author = {Mark Skandera and Daniel Soskin},
title = {Permanental inequalities for totally positive matrices},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {1},
doi = {10.37236/13098},
zbl = {1559.15009},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13098/}
}
TY - JOUR
AU - Mark Skandera
AU - Daniel Soskin
TI - Permanental inequalities for totally positive matrices
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/13098/
DO - 10.37236/13098
ID - 10_37236_13098
ER -
%0 Journal Article
%A Mark Skandera
%A Daniel Soskin
%T Permanental inequalities for totally positive matrices
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/13098/
%R 10.37236/13098
%F 10_37236_13098
Mark Skandera; Daniel Soskin. Permanental inequalities for totally positive matrices. The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/13098
