Inductive and injective proofs of log concavity results
type: Item
instance of: scholarly article
title: Inductive and injective proofs of log concavity results
zbMATH Open document ID: 0658.05003
DOI: 10.1016/0012-365X(88)90120-3
author: Bruce E. Sagan
published in: Discrete Mathematics
publication date: 1988-01-01T00:00:00Z
review text: A necessary condition is obtained for every row of a triangular array to be log concave, where a sequence \(\{a_ k\}_{0\leq k\leq n}\) is called log concave if \(a_{k-1}a_{k+1}\leq a^ 2_ k,\) for all k, \(0<k<n\). This result is used to inductively construct injections showing the log concavity of the binomial coefficients and Stirling numbers of both kinds. These proofs are related to graphical interpretation of these numbers by Wilf.
Mathematics Subject Classification ID: 05A10
zbMATH DE Number: 4075067
zbMATH Keywords: log concavity
zbMATH Keywords: triangular array
zbMATH Keywords: binomial coefficients
zbMATH Keywords: Stirling numbers
Wikidata QID: Q114215634
MaRDI profile type: Publication
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full work available at URL: 0012-365x(88)90120-3
OpenAlex ID: W2093824255
description: scientific article; zbMATH DE number 4075067