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-Roichman, Vershik-Vserminov and others. In a recent work of Brenti- Reiner-Roichman it is explained that palindromes in Mitsuhashi's generating set play a role similar to that of re ections 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.

References in corpus (1)

• The q-analogue of the alternating groups and its representations

Cited by in corpus (4)

• A Poset Structure on the Alternating Group Generated by 3-Cycles
• Nakayama Automorphism and Rigidity of Dual Reflections Group Coactions
• The absolute order of a permutation representation of a Coxeter group
• Normal subgroups of iterated wreath products of symmetric groups and alternating with symmetric groups