Chords in a circle and linear algebra over GF(2)
type: Item
instance of: scholarly article
title: Chords in a circle and linear algebra over GF(2)
zbMATH Open document ID: 0552.05001
DOI: 10.1016/0097-3165(84)90048-7
author: Gadi Moran
published in: Journal of Combinatorial Theory. Series A
publication date: 1984-01-01T00:00:00Z
review text: \textit{M. Cohn} and \textit{A. Lempel} [J. Comb. Theory, Ser. A 13, 83-89 (1972; Zbl 0314.05005)] showed that if \(\tau \in S_ n\) is an n-cycle and \(\sigma \in S_ n\) is a product of disjoint transpositions, then the number of orbits of \(\sigma\) \(\tau\) is one more than the nullity of a certain matrix over GF(2), obtained as an incidence matrix for carefully chosen chords of a circle. Here, a new proof is given, based on the study of a certain boolean measure on the boolean algebra of subsets of the circle.
reviewed by: William H. Gustafson
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 20B30
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 3878928
zbMATH Keywords: boolean measures
zbMATH Keywords: chord intersection matrix
zbMATH Keywords: permutations
MaRDI profile type: Publication
full work available at URL: 0097-3165(84)90048-7
OpenAlex ID: W2068057794
cites work: Cycle decomposition by transpositions
cites work: Q3746003
cites work: Cycle decomposition by disjoint transpositions
description: scientific article; zbMATH DE number 3878928