2014/07/21 by Bridget Eileen Tenner, Tenner, Bridget Eileen
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #semigroups and automata theory #Algorithms and Data Compression
paper · pdf · doi:10.48550/arxiv.1407.5636
We compute the expected number of commutations appearing in a reduced word for the longest element in the symmetric group. The asymptotic behavior of this value is analyzed and shown to approach the length of the permutation, meaning that nearly all positions in the reduced word are expected to support commutations. Finally, we calculate the asymptotic frequencies of commutations, consecutive noncommuting pairs, and long braid moves.