The descent statistic on involutions is not log-concave

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.

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