In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group Sym(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. © 2013 Springer Science+Business Media New York.
Bamberg, J., Gill, N., Hayes, T., Helfgott, H., Seress, Á., Spiga, P. (2014). Bounds on the diameter of Cayley graphs of the symmetric group. JOURNAL OF ALGEBRAIC COMBINATORICS, 40(1), 1-22 [10.1007/s10801-013-0476-3].
Bounds on the diameter of Cayley graphs of the symmetric group
SPIGA, PABLOUltimo
2014
Abstract
In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group Sym(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. © 2013 Springer Science+Business Media New York.
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