Title: Permanental inequalities for totally positive matrices Show Chinese title

Title: 完全正矩阵的永久不等式

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 $\mathbb{Z}[x_{1,1},x_{1,2},...,x_{n,n}]$ which evaluate positively on the set of all totally positive $n \times n$ matrices. Show Chinese abstract

Abstract: 我们表征了在所有完全正矩阵集合上有界的(广义)子矩阵的永久式的比值。 这提供了Fallat、Gekhtman和Johnson[{\em 高级 应用数学} {\bf 30} 第3期，(2003) 第442--470页]关于矩阵余子式比值结果的永久式类比。 我们还通过表征在所有完全正$n \times n$矩阵上正确定值的$\mathbb{Z}[x_{1,1},x_{1,2},...,x_{n,n}]$中的单项式的差值，扩展了Drake、Gerrish和第一作者[{\em 电子. 组合学杂志,} {\bf 11} 第1期，(2004) 注释6]的工作。