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.
M. Barnabei, F. Bonetti, M. Silimbani (2009). The descent statistic on involutions is not log-concave. EUROPEAN JOURNAL OF COMBINATORICS, 30, 11-16 [10.1016/j.ejc.2008.03.003].
The descent statistic on involutions is not log-concave
BARNABEI, MARILENA;BONETTI, FLAVIO;SILIMBANI, MATTEO
2009
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.File in questo prodotto:
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