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arXiv · 1602.08328

On the number of commutation classes of the longest element in the symmetric group

Hugh Denoncourt·Dana C. Ernst·Dustin Story
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Abstract

Using the standard Coxeter presentation for the symmetric group $S_n$, two reduced expressions for the same group element are said to be commutation equivalent if we can obtain one expression from the other by applying a finite sequence of commutations. The resulting equivalence classes of reduced expressions are called commutation classes. How many commutation classes are there for the longest element in $S_n$?

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Hugh Denoncourt, Dana C. Ernst, Dustin Story. 2016-01-25. On the number of commutation classes of the longest element in the symmetric group. https://arxiv.org/abs/1602.08328

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