An atomic model of the graph of permutations linked by transpositions
type: Item
instance of: scholarly article
title: An atomic model of the graph of permutations linked by transpositions
author: Achim Kehrein
author: Frank Zimmer
author: Nicolas Fischöder
published in: Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV)
publication date: 2022-10-24T00:00:00Z
review text: The authors study the Cayley graph for the symmetric group, generated by transpositions. (This graph has relevance in campanology as well, but the authors do not investigate this connection.) They note that minimal product length in generators is determined by cycle structure; thus a partition of permutations by minimal word length can be refined into a partition by conjugacy classes. The author study (using language borrowed from the theory of atoms) such ``shells'' of elements of same minimal word length, as well as connections between different shells. Using standard ``energy minimization'' methods, They study how these graphs could be embedded, for \(n=3,4\) into \(\mathbb{R}^3\) in pleasing configurations and illustrate these through images. (It is noted that this approach performs less well in degree 5.)
reviewed by: A. Hulpke
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20B30
zbMATH DE Number: 7606353
zbMATH Keywords: symmetric groups
zbMATH Keywords: Cayley graph
MaRDI profile type: Publication
full work available at URL: dmvm-2022-0059
OpenAlex ID: W4293071125
DOI: 10.1515/DMVM-2022-0059
Recommended article: Transposition Graphs: An Intuitive Approach to the Parity Theorem for Permutations
Recommended article: On permutation graphs
Recommended article: Q4954629
Recommended article: A transposition factorization of walk-permutations in graphs
Recommended article: A theorem on permutation graphs with applications
Recommended article: Permutations in Coinductive Graph Representation
Recommended article: Transitivity and connectivity of permutations
Recommended article: Q4691626
Recommended article: The combinatorial compound of permutation matrix and graphical representation
Recommended article: Q4723777
description: scientific article; zbMATH DE number 7606353