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Generator sets for the alternating group. (English) Zbl 1295.05269
Summary: 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 F. Brenti et al. [J. Comb. Theory, Ser. A 115, No. 5, 845–877 (2008; Zbl 1211.20035)], 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.

05E15 Combinatorial aspects of groups and algebras (MSC2010)
20B30 Symmetric groups
20F05 Generators, relations, and presentations of groups
20F55 Reflection and Coxeter groups (group-theoretic aspects)
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