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EnglishWe exploit Krattenthaler’s bijection between the set Sn(3-1-2) of permutations in Sn avoiding the classical pattern 3-1-2 and Dyck n-paths to study the joint distribution over the set Sn(3-1-2) of a given consecutive pattern of length 3 and of descents. We utilize a involution on Dyck paths due to E. Deutsch to show that these consecutive patterns split into 3 equidistribution classes. In addition, we state equidistribution theorems concerning quadruplets of statistics relative to occurrences of consecutive patterns of length 3 and of descents in a permutation.
| Titolo: | The joint distribution of consecutive patterns and descents in permutations avoiding 3-1-2 |
| Autore/i: | BARNABEI, MARILENA; BONETTI, FLAVIO; SILIMBANI, MATTEO |
| Autore/i Unibo: | |
| Anno: | 2010 |
| Rivista: | |
| Digital Object Identifier (DOI): | 10.1016/j.ejc.2009.11.011 |
| Abstract: | We exploit Krattenthaler’s bijection between the set Sn(3-1-2) of permutations in Sn avoiding the classical pattern 3-1-2 and Dyck n-paths to study the joint distribution over the set Sn(3-1-2) of a given consecutive pattern of length 3 and of descents. We utilize a involution on Dyck paths due to E. Deutsch to show that these consecutive patterns split into 3 equidistribution classes. In addition, we state equidistribution theorems concerning quadruplets of statistics relative to occurrences of consecutive patterns of length 3 and of descents in a permutation. |
| Data prodotto definitivo in UGOV: | 2010-05-12 10:46:29 |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/11585/89290
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