Dyck tilings of type $D$

Abstract

We introduce and study cover-inclusive and cover-exclusive Dyck tilings of type $D$. It is shown that the generating functions of Dyck tilings of type $D$ are expressed in terms of the generating function of ballot tilings of type $B$. We introduce link patterns of type $D$ and plane trees for a ballot path, and construct a map from trees to $\mathbb{Z}[q]$. This map gives the generating function of cover-inclusive Dyck tilings of type $D$ associated to the ballot path.

14 pages

References in corpus (4)

• Fully Packed Loops in a triangle: matchings, paths and puzzles
• Kazhdan-Lusztig polynomials for the Hermitian symmetric pair $(B_N,A_{N-1})$
• Ballot tilings and increasing trees
• Symmetric Dyck tilings, ballot tableaux and tree-like tableaux of shifted shapes