Dyck tilings, increasing trees, descents, and inversions

Authors:
Jang Soo Kim;Karola Mészáros;Greta Panova;David B. Wilson
Affiliations:
University of Minnesota, United States;University of Michigan, United States;University of California, Los Angeles, United States;Microsoft Research, United States
Venue:
Journal of Combinatorial Theory Series A
Year:
2014

Citing 5
Cited 0

q-Hook length formulas for forests

Journal of Combinatorial Theory Series A
Regular Article: New Euler驴Mahonian Statistics on Permutations and Words

Advances in Applied Mathematics
Varieties of Increasing Trees

CAAP '92 Proceedings of the 17th Colloquium on Trees in Algebra and Programming
Proofs of two conjectures of Kenyon and Wilson on Dyck tilings

Journal of Combinatorial Theory Series A
Dyck tableaux

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Cover-inclusive Dyck tilings are tilings of skew Young diagrams with ribbon tiles shaped like Dyck paths, in which tiles are no larger than the tiles they cover. These tilings arise in the study of certain statistical physics models and also Kazhdan-Lusztig polynomials. We give two bijections between cover-inclusive Dyck tilings and linear extensions of tree posets. The first bijection maps the statistic (area+tiles)/2 to inversions of the linear extension, and the second bijection maps the ''discrepancy'' between the upper and lower boundary of the tiling to descents of the linear extension.