Permanent formulae from the Veronesean
type: Item
instance of: scholarly article
title: Permanent formulae from the Veronesean
zbMATH Open document ID: 1301.15007
author: David G. Glynn
published in: Designs, Codes and Cryptography
publication date: 2013-05-30T00:00:00Z
review text: There is an obvious similarity between the two formulae for the permanent of a square matrix given by \textit{H. J. Ryser} [Combinatorial mathematics. Washington, D.C.: Mathematical Association of America (1963; Zbl 0112.24806)] and \textit{D. G. Glynn} [Eur. J. Comb. 31, No. 7, 1887--1891 (2010; Zbl 1209.15012)]. In this paper the author clarifies this relationship, making use of classic algebraic concepts (theorem of P. Serret), dependencies on the Veronesean (Veronese variety) and polarization identities for symmetric tensors. Using this, it is possible to obtain infinitely many such formulae.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 05E99
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 94B60
zbMATH DE Number: 6168437
zbMATH Keywords: permanent
zbMATH Keywords: matrix
zbMATH Keywords: Veronesean
zbMATH Keywords: polarization identity
zbMATH Keywords: symmetric tensor
Wikidata QID: Q56806476
reviewed by: Rabe von Randow
MaRDI profile type: Publication
full work available at URL: s10623-012-9618-1
OpenAlex ID: W2101538406
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DOI: 10.1007/S10623-012-9618-1
description: scientific article; zbMATH DE number 6168437