The descent statistic on involutions is not log-concave

Barnabei, Marilena; Bonetti, Flavio; Silimbani, Matteo

The descent statistic on involutions is not log-concave

Authors

Barnabei, Marilena

Bonetti, Flavio

Silimbani, Matteo

Description

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.
10 pages