Bounds on the diameter of Cayley graphs of the symmetric group

John Bamberg, Nick Gill, Thomas Hayes, Harald Helfgott, Ákos Seress, Pablo Spiga

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Abstract

In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group of degree n, the word length in terms of S of every permutation is bounded above by a polynomial of n. We prove this conjecture for sets of generators containing a permutation fixing at least 37% of the points.
Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalJournal of Algebraic Combinatorics
Volume40
Issue number1
DOIs
Publication statusPublished - 2014

Keywords

  • math.GR
  • math.CO

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