Vol. 13, No. 4, 2020

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Conjugation diameter of the symmetric groups

Assaf Libman and Charlotte Tarry

Vol. 13 (2020), No. 4, 655–672
Abstract

The conjugation diameter of a group G is the largest diameter of its Cayley graphs with respect to conjugation-invariant generating sets. It is a strong form of the extensively studied concept of the diameter of G. We compute the conjugation diameter of the symmetric groups.

Keywords
conjugation diameter, symmetric groups
Mathematical Subject Classification 2010
Primary: 05E15, 20B30
Milestones
Received: 4 March 2020
Revised: 10 May 2020
Accepted: 25 June 2020
Published: 20 November 2020

Communicated by Kenneth S. Berenhaut
Authors
Assaf Libman
Institute of Mathematics
University of Aberdeen
King’s College
Aberdeen
United Kingdom
Charlotte Tarry
Institute of Mathematics
University of Aberdeen
King’s College
Aberdeen
United Kingdom