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On the expected number of commutations in reduced words. (English) Zbl 1321.05007
Summary: 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.

MSC:
05A05 Permutations, words, matrices
05C82 Small world graphs, complex networks (graph-theoretic aspects)
68R15 Combinatorics on words
20B30 Symmetric groups
Keywords:
symmetric group
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