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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