Geodesic
Double-dimer pairings and skew Young diagrams
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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 $\varepsilon\to0$.
DOI : 10.37236/617
Classification : 05A19, 05B45, 60C05, 82B20, 05C05, 05C50
Mots-clés : skew Young diagram, double-dimer model, grove, spanning tree 
@article{10_37236_617,
     author = {Richard W. Kenyon and David B. Wilson},
     title = {Double-dimer pairings and skew {Young} diagrams},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/617},
     zbl = {1247.05025},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/617/}
}
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Richard W. Kenyon; David B. Wilson. Double-dimer pairings and skew Young diagrams. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/617

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