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The double-dimer model and skew Young diagrams

The double-dimer model and skew Young diagrams. Richard W. Kenyon David B. Wilson Brown University Microsoft Research. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A A A A A. The double-dimer model. Kasteleyn matrix. 1.

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The double-dimer model and skew Young diagrams

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  1. The double-dimer model and skew Young diagrams Richard W. Kenyon David B. Wilson Brown University Microsoft Research TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAAA

  2. The double-dimer model

  3. Kasteleyn matrix 1 1 3 2 2 3 5 5 4 4 6 8 9 9 6 7 8 7 (bipartite version)

  4. 4 5 3 2 6 1 4 5 4 5 3 3 2 6 2 6 1 1 The double-dimer model

  5. 4 4 4 5 5 5 3 3 3 2 2 2 6 6 6 1 1 1 The double-dimer model

  6. 4 5 3 2 6 1 4 5 3 2 6 1 The double-dimer model Assume (wlog) that nodes alternate in color

  7. 5 4 5 4 5 4 5 4 3 3 3 3 6 6 6 6 1 2 1 2 1 2 1 2 Probability of pairing in DD model 4 5 3 2 6 1 5 4 3 6 1 2

  8. 5 5 5 4 4 4 5 4 5 4 5 4 5 5 4 4 3 3 3 3 3 3 3 3 6 6 6 6 6 6 6 6 1 1 1 2 2 2 1 2 1 2 1 2 1 1 2 2 Other connection topologies For six nodes, get all 5 connection topologies

  9. What if there are more nodes? With 2n nodes, # crossing types is nth Catalan number. Can we compute all their probabilities?

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