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.: AAAA A A A A AA A A A A

2. The double-dimer model

3. Kasteleyn matrix 1 1 2 2 3 3 4455 6 6 7 7 8 89 9 (bipartite version)

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

5. 6 1 2 5 4 3 6 1 2 5 4 3 6 1 2 5 4 3

6. 6 1 2 5 4 3 6 1 2 5 4 3 Assume (wlog) that nodes alternate in color

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

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

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