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{\bf Richard W. Kenyon and David B. Wilson}
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{\bf Double-Dimer Pairings and Skew Young Diagrams}
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We study the number of tilings of skew Young diagrams by ribbon tiles
shaped like Dyck paths, in which the tiles are ``vertically
decreasing''. We use these quantities to compute pairing
probabilities in the double-dimer model: Given a planar bipartite
graph~$G$ with special vertices, called nodes, on the outer face, the
double-dimer model is formed by the superposition of a uniformly
random dimer configuration (perfect matching) of~$G$ together with a
random dimer configuration of the graph formed from~$G$ by deleting
the nodes. The double-dimer configuration consists of loops, doubled
edges, and chains that start and end at the boundary nodes. We are
interested in how the chains connect the nodes. An interesting
special case is when the graph is $\varepsilon(\mathbb Z\times\mathbb
N)$ and the nodes are at evenly spaced locations on the
boundary~$\mathbb R$ as the grid spacing~$\varepsilon\to0$.
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