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arXiv · 1205.1596

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.

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John Bamberg, Nick Gill, Thomas Hayes, Harald Helfgott, Ákos Seress, Pablo Spiga. 2012-05-08. Bounds on the diameter of Cayley graphs of the symmetric group. https://arxiv.org/abs/1205.1596

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