Proofs of Two Conjectures of Kenyon and Wilson on Dyck Tilings

Jang Soo Kim (김장수)

School of Mathematics, University of Minnesota, Minneapolis, MN, USA

School of Mathematics, University of Minnesota, Minneapolis, MN, USA

2012/7/27

*Fri*4PM-5PMRecently, 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

This talk is based on the following paper: arxiv:1108.5558.

^{-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.

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