The Eulerian distribution on self evacuated involutions
Marilena Barnabei, Flavio Bonetti, Matteo Silimbani
TL;DR
This paper investigates the Eulerian distribution on self evacuated involutions, providing combinatorial properties, explicit formulas for generating polynomial coefficients, and analyzing fixed-point free cases.
Contribution
It offers new combinatorial insights and explicit formulas for the Eulerian distribution on self evacuated involutions and their fixed-point free subset.
Findings
Derived combinatorial properties of the generating polynomial.
Provided explicit formulas for coefficients of the distribution.
Analyzed the subset of fixed-point free self evacuated involutions.
Abstract
We present an extensive study of the Eulerian distribution on the set of self evacuated involutions, namely, involutions corresponding to standard Young tableaux that are fixed under the Schtzenberger map. We find some combinatorial properties for the generating polynomial of such distribution, together with an explicit formula for its coefficients. Afterwards, we carry out an analogous study for the subset of self evacuated involutions without fixed points.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Mathematical Identities