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

作者：Barnabei Marilena^*; Bonetti Flavio; Elizalde Sergi; Silimbani Matteo

来源：Journal of Combinatorial Theory - Series A, 2014, 128: 132-148.

DOI：10.1016/j.jcta.2014.08.002

• Restricted involution
• Descent
• Major index
• Integer partition
• Lattice path

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 771 into partitions of m whose Young diagram fits inside a [n/2] x [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.

• 出版日期2014-11