שלחו לחבר

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