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

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:128

Article

Barnabei, Marilena¹  Bonetti, Flavio¹  Elizalde, Sergi²  Silimbani, Matteo¹ 

[1] Univ Bologna, Dipartmento Matemat, I-40126 Bologna, Italy

[2] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA

关键词: Restricted involution;    Descent;    Major index;    Integer partition;    Lattice path;   

DOI  :  10.1016/j.jcta.2014.08.002

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free