Bounds on the diameter of Cayley graphs of the symmetric group

Bamberg, John; Gill, Nick; Hayes, Thomas P.; Helfgott, Harald A.; Seress, Akos and Spiga, Pablo (2014). Bounds on the diameter of Cayley graphs of the symmetric group. Journal of Algebraic Combinatorics, 40(1) pp. 1–22.

DOI: https://doi.org/10.1007/s10801-013-0476-3

Abstract

In this paper we are concerned with the conjecture that, for any set of generators of the symmetric group , the word length in terms of of every permutation is bounded above by a polynomial of . We prove this conjecture for sets of generators containing a permutation fixing at least 37% of the points.

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