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# The Worpitzky identity for the groups of signed and even-signed permutations

Seminar
Speaker
Eli Bagno (Jerusalem College of Technology)
Date
06/12/2020 - 15:30 - 14:00
Place
Zoom
Abstract

The well-known Worpitzky identity provides a connection between two bases of $\mathbb{Q}[x]$: The standard basis $(x+1)^n$ and the binomial basis ${{x+n-i} \choose {n}}$, where the Eulerian numbers for the Coxeter group of type $A$ (the symmetric group) serve as the entries of the transformation matrix.

Brenti has generalized this identity to the Coxeter groups of types $B$ and $D$ (signed and even-signed permutations groups, respectively) using generatingfunctionology.

Motivated by Foata-Schützenberger and Rawlings' proof for the Worpitzky identity in the symmetric group, we provide combinatorial proofs of this identity and for its $q$-analogue in the Coxeter groups of types $B$ and $D$. Our proofs utilize the language of $P$-partitions for the $B_n$ and $D_n$ posets introduced by Chow and Stembridge, respectively.

Joint work with David Garber and Mordechai Novick.

תאריך עדכון אחרון : 01/12/2020