Inequalities for the gamma function with applications to permanents
type: Item
instance of: scholarly article
title: Inequalities for the gamma function with applications to permanents
zbMATH Open document ID: 0863.33001
DOI: 10.1016/0012-365X(94)00340-O
author: Peter J. Grabner
author: Uwe T. Zimmermann
author: Robert F. Tichy
published in: Discrete Mathematics
publication date: 1997-06-10T00:00:00Z
review text: The theorem of Bohr-Mollerup (1922) characterizes the gamma-function through the functional equation and log-convexity. The authors show that \(f(x) = \log (\Gamma (x+1))/x\) can be characterized by the corresponding functional equation, concavity and \(f(1) = 0\). This result is used to prove some upper bounds for the permanent of a \(0-1\)-matrix, as e.g. \(\text{per} (A) \leq (\Gamma (\alpha /n + 1))^{n^2/ \alpha}\). For related bounds see also \textit{R. A. Brualdi}, \textit{J. L. Goldwasser} and \textit{T. S. Michael}, J. Comb. Theory, Ser. A 47, No. 2, 207-245 (1988; Zbl 0647.15002)].
reviewed by: Ulrich Stadtmüller
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 906891
zbMATH Keywords: Bohr-Mollerup-theorem
zbMATH Keywords: gamma-function
zbMATH Keywords: permanents
MaRDI profile type: Publication
cites work: Fast algorithms for the maximum convolution problem
cites work: Q3274282
cites work: Q5810675
cites work: Matching theory
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cites work: A short proof of Minc's conjecture
cites work: Maximum permanents of matrices of zeros and ones
full work available at URL: 0012-365x(94)00340-o
OpenAlex ID: W2008574866
description: scientific article; zbMATH DE number 906891