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EnglishWe 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 a ⌊n/2⌋×⌈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.
| Titolo: | Descent sets on 321-avoiding involutions and hook decompositions of partitions |
| Autore/i: | BARNABEI, MARILENA; BONETTI, FLAVIO; Sergi Elizalde; SILIMBANI, MATTEO |
| Autore/i Unibo: | |
| Anno: | 2014 |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jcta.2014.08.002 |
| 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 a ⌊n/2⌋×⌈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. |
| Data prodotto definitivo in UGOV: | 2014-10-08 10:48:50 |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/11585/353320
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