Mixing and covering in the symmetric groups
type: Item
instance of: scholarly article
title: Mixing and covering in the symmetric groups
zbMATH Open document ID: 0940.20007
author: Uzi Vishne
published in: Journal of Algebra
publication date: 2000-05-04T00:00:00Z
review text: The covering of symmetric and alternating groups by powers of conjugacy classes is studied in this paper. Particular emphasis is laid on mixing which means that the computation of the powers is viewed as a stochastic process by taking samples out of the conjugacy class and then multiply them. In particular, the conjugacy class \([2^{n/2}]\) of the symmetric group \(S_n\) is studied; some new character identities are derived from the computation of \([2^{n/2}]^2\), also the power \([2^{n/2}]^3\) is computed. The results are applied to a certain classification of \(3\)-colored \(3\)-regular graphs.
Mathematics Subject Classification ID: 20B30
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 60E99
zbMATH DE Number: 1218710
zbMATH Keywords: symmetric groups
zbMATH Keywords: alternating groups
zbMATH Keywords: conjugacy classes
zbMATH Keywords: coverings
zbMATH Keywords: mixings
zbMATH Keywords: uniform distributions
zbMATH Keywords: mixing times
zbMATH Keywords: random processes
zbMATH Keywords: characters
zbMATH Keywords: \(3\)-regular graphs
zbMATH Keywords: \(3\)-colorable graphs
MaRDI profile type: Publication
OpenAlex ID: W2119281850
cites work: Q3695451
cites work: Q4102043
cites work: Q4152726
cites work: Q3995195
cites work: Generating a random permutation with random transpositions
cites work: Products of conjugacy classes in groups
cites work: On the number of rim hook tableaux
cites work: Q3243274
cites work: Random Cayley graphs and expanders
DOI: 10.1006/JABR.1997.7366
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description: scientific article; zbMATH DE number 1218710