On the Alternating runs polynomial in type B and D Coxeter Groups

Abstract

Wilf showed that the the alternating runs polynomial $R_n(t)$ counting the number of permutations in the Symmetric group is divisible by $(1+t{)}^m$ where $m=\lfloor (n-2)/2\rfloor$. Recently, Bóna gave a group action based proof. Type B and D analogues of Wilf's result are known. In this note, we extend Bóna's proof to prove the type B and D analogue.

9 pages. Added a section on applications of this result to refining moment-type identities

References in corpus (1)

• Generating functions of permutations with respect to their alternating runs