An inequality on paths in a grid
type: Item
instance of: scholarly article
title: An inequality on paths in a grid
zbMATH Open document ID: 0772.05018
DOI: 10.1016/0097-3165(92)90026-Q
author: Stein Krogdahl
author: István Beck
published in: Journal of Combinatorial Theory. Series A
publication date: 1993-01-17T00:00:00Z
review text: An inequality on paths in a grid is given in the paper. Let \((c_{i,j})\) be a positive \(n\times m\) log supermodular matrix, i.e., \(c_{i,j}\cdot c_{i+1,j+1}\geq c_{i+1,j}\cdot c_{i,j+1}\). Then there exists a path from \(c_{1,1}\) to \(c_{n,m}\) whose average dominates that of all the entries of the matrix \((c_{i,j})\).
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 06A99
zbMATH DE Number: 96581
zbMATH Keywords: partially ordered set
zbMATH Keywords: inequality
zbMATH Keywords: path
zbMATH Keywords: grid
zbMATH Keywords: log supermodular matrix
reviewed by: Shenquan Xie
MaRDI profile type: Publication
cites work: On log concave sequences
cites work: Combinatorial applications of an inequality from statistical mechanics
description: scientific article; zbMATH DE number 96581