2010/10/26 by Aviv Rotbart, Rotbart, Aviv
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1010.5288
arxiv created 2010/10/26 · arxiv updated 2010/10/27
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.