The Eulerian distribution on centrosymmetric involutions
Marilena Barnabei, Flavio Bonetti, Matteo Silimbani
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 Sch$\ddot{\textrm{u}}$tzenberger 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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