New Eulerian Numbers of Type $D$

Anna Borowiec, Wojciech Młotkowski

Abstract


We introduce a new array of type $D$ Eulerian numbers, different from that studied by Brenti, Chow and Hyatt. We find in particular the recurrence relation, Worpitzky formula and the generating function. We also find the probability distributions whose moments are Eulerian polynomials of type $A$, $B$ and $D$.


Keywords


Eulerian numbers, Signed permutations, Moments of a probability measure

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