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

Hiranya Kishore Dey; Sivaramakrishnan Sivasubramanian

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

Combinatorics 2021-11-29 v3

Authors: Hiranya Kishore Dey , Sivaramakrishnan Sivasubramanian

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, B\'{o}na gave a group action based proof. Type B and D analogues of Wilf's result are known. In this note, we extend B\'{o}na's proof to prove the type B and D analogue.

Keywords

permutations

Cite

@article{arxiv.2009.02901,
  title  = {On the Alternating runs polynomial in type B and D Coxeter Groups},
  author = {Hiranya Kishore Dey and Sivaramakrishnan Sivasubramanian},
  journal= {arXiv preprint arXiv:2009.02901},
  year   = {2021}
}

Comments

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

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

Abstract

Keywords

Cite

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