## Jang Soo Kim (김장수), Proofs of Two Conjectures of Kenyon and Wilson on Dyck Tilings

Proofs of Two Conjectures of Kenyon and Wilson on Dyck Tilings
Jang Soo Kim (김장수)
School of Mathematics, University of Minnesota, Minneapolis, MN, USA
2012/7/27 Fri 4PM-5PM
Recently, Kenyon and Wilson introduced a certain matrix M in order to compute pairing probabilities of what they call the double-dimer model. They showed that the absolute value of each entry of the inverse matrix M-1 is equal to the number of certain Dyck tilings of a skew shape. They conjectured two formulas on the sum of the absolute values of the entries in a row or a column of M-1. In this talk we prove the two conjectures. As a consequence we obtain that the sum of the absolute values of all entries of M-1 is equal to the number of complete matchings. We also find a bijection between Dyck tilings and complete matchings.
This talk is based on the following paper: arxiv:1108.5558.

Tags: