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arXiv · 1401.3011

Descent sets on 321-avoiding involutions and hook decompositions of partitions

Marilena Barnabei·Flavio Bonetti·Sergi Elizalde·Matteo Silimbani
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Abstract

We show that the distribution of the major index over the set of involutions in S_n that avoid the pattern 321 is given by the q-analogue of the n-th central binomial coefficient. The proof consists of a composition of three non-trivial bijections, one being the Robinson-Schensted correspondence, ultimately mapping those involutions with major index m into partitions of m whose Young diagram fits inside an n/2 by n/2 box. We also obtain a refinement that keeps track of the descent set, and we deduce an analogous result for the comajor index of 123-avoiding involutions.

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Marilena Barnabei, Flavio Bonetti, Sergi Elizalde, Matteo Silimbani. 2014-01-13. Descent sets on 321-avoiding involutions and hook decompositions of partitions. https://arxiv.org/abs/1401.3011

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