We establish a combinatorial connection between the sequence $(i_{n,k})$ counting the involutions on $n$ letters with $k$ descents and the sequence $(a_{n,k})$ enumerating the semistandard Young tableaux on $n$ cells with $k$ symbols. This allows us to show that the sequences $(i_{n,k})$ are not log-concave for some values of $n$, hence answering a conjecture due to F. Brenti.
Titolo: | The descent statistic on involutions is not log-concave |
Autore/i: | BARNABEI, MARILENA; BONETTI, FLAVIO; SILIMBANI, MATTEO |
Autore/i Unibo: | |
Anno: | 2009 |
Rivista: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.ejc.2008.03.003 |
Abstract: | We establish a combinatorial connection between the sequence $(i_{n,k})$ counting the involutions on $n$ letters with $k$ descents and the sequence $(a_{n,k})$ enumerating the semistandard Young tableaux on $n$ cells with $k$ symbols. This allows us to show that the sequences $(i_{n,k})$ are not log-concave for some values of $n$, hence answering a conjecture due to F. Brenti. |
Data prodotto definitivo in UGOV: | 2009-02-09 10:13:13 |
Appare nelle tipologie: | 1.01 Articolo in rivista |
File in questo prodotto:
Eventuali allegati, non sono esposti
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.