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- W2952905962 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 paper 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." @default.
- W2952905962 created "2019-06-27" @default.
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- W2952905962 date "2011-08-29" @default.
- W2952905962 modified "2023-09-23" @default.
- W2952905962 title "Proofs of two conjectures of Kenyon and Wilson on Dyck tilings" @default.
- W2952905962 hasPublicationYear "2011" @default.
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