An inequality conjectured by Hajela and Seymour arising in combinatorial geometry
type: Item
instance of: scholarly article
title: An inequality conjectured by Hajela and Seymour arising in combinatorial geometry
zbMATH Open document ID: 0628.26014
DOI: 10.1007/BF02579248
author: B. F. Logan
author: Henry Landau
author: Larry Shepp
published in: Combinatorica
publication date: 1985-01-01T00:00:00Z
review text: In a recent paper, \textit{D. Hajela} and \textit{P. Seymour} [same journal 5, 205-214 (1985; Zbl 0597.05003)] proved that for \(0\leq b_ 1\leq b_ 2\leq 1\), \(\alpha =(\log_ 2 3)/2\), \[ b_ 1^{\alpha}b_ 2^{\alpha}+(1- b_ 1)^{\alpha}b_ 2^{\alpha}+(1-b_ 1)^{\alpha}(1-b_ 2)^{\alpha}\geq 1, \] and drew from this inequality a variety of interesting results in combinatorial geometry. They also conjectured a generalization of the inequality to n variables, which they showed to imply a lower bound on the number of different sequences obtained when members of n sets of zero-one sequences are added to one another. We prove their conjecture, not easy to verify even for small values of n, using complex-variable theory.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A37
zbMATH DE Number: 4021494
zbMATH Keywords: application in combinatorial geometry
zbMATH Keywords: inequality
MaRDI profile type: Publication
cites work: Counting points in hypercubes and convolution measure algebras
cites work: AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION
description: scientific article; zbMATH DE number 4021494