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CM-AMO SEMINAR | The Entropy of Dimer or Monomer-Dimer Systems on Lattices

Tuesday, October 15, 2013
4:00 AM
335 West Hall

How many ways are there of covering a chess board with dominoes (the dimer problem) or covering a fraction p of the squares (the monomer-dimer problem). Dominoes cover two neighboring squares, and must not overlap. This easily generalizes to the same questions on arbitrary lattices in any dimension. We discuss results (mostly very new) , proved, numerical, conjectured, particularly for d-dimensional rectangular lattices. There is a wonderful conjecture. Certainly no familiarity with dimer problems is assumed.