Séminaire Lotharingien de Combinatoire, B65b (2011), 16 pp.

Aviv Rotbart

Generator Sets for the Alternating Group

Abstract. Although the alternating group is an index 2 subgroup of the symmetric group, there is no generating set that gives a Coxeter structure on it. Various generating sets were suggested and studied by Bourbaki, Mitsuhashi, Regev and Roichman, Vershik and Vserminov, and others. In a recent work of Brenti, Reiner and Roichman, it is explained that palindromes in Mitsuhashi's generating set play a role similar to that of reflections in a Coxeter system.

We study in detail the length function with respect to the set of palindromes. Results include an explicit combinatorial description, a generating function, and an interesting connection to Broder's restricted Stirling numbers.

Received: November 4, 2010. Accepted: April 29, 2011. Final Version: April 29, 2011.

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