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 colamn 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 bijectio between Dyck tilings and complete matchings.
| Original language | English |
|---|---|
| Pages (from-to) | 361-372 |
| Number of pages | 12 |
| Journal | Discrete Mathematics and Theoretical Computer Science |
| State | Published - 2012 |
| Externally published | Yes |
| Event | 24th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2012 - Nagoya, Japan Duration: 30 Jul 2012 → 3 Aug 2012 |
Keywords
- Dyck paths
- Dyck tilings
- Hermite histories
- Matchings
- Orthogonal polynomials
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