Generalized Dyck tilings

zed Dyck tilings (Extended Abstract) Matthieu Josuat-Verg´es1∗ and Jang Soo Kim 2† 1 IGM, Universit´e de Marne-la-Vall´ee, France 2 Department of Mathematics, Sungkyunkwan University, Suwon 440-746, South Korea. Recently, Kenyon and Wilson introduced Dyck tilings, which are certain tilings of the region between two Dyck paths. The enumeration of Dyck tilings is related with hook formulas for forests and the combinatorics of Hermite polynomials. The first goal of this work is to give an alternative point of view on Dyck tilings by making use of the weak order and the Bruhat order on permutations. Then we introduce two natural generalizations: k-Dyck tilings and symmetric Dyck tilings. We are led to consider Stirling permutations, and define an analogue of the Bruhat order on them. We show that certain families of k-Dyck tilings are in bijection with intervals in this order. We enumerate symmetric Dyck tilings and show that certain families of symmetric Dyck tilings are in bijec...

• Type: Journal
• Year: 2016
• Where: EJC
• Authors: Matthieu Josuat-Vergès, Jang Soo Kim
• Keywords: EJC 2016, Information Technology