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

Eli Bagno, David Garber, Mordechai Novick

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 $\left(\genfrac{}{}{0ex}{}{x+n-i}{n}\right)$, where the…