Title    name KAIST Discrete Math Seminar     Title Proofs of Two Conjectures of Kenyon and Wilson on Dyck Tilings   Speaker Kim, Jangsoo   Date 2012-07-27   Host   Place KAIST   File     Abstract : 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.

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