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Dimers on two types of lattices on the Klein bottle. (English) Zbl 1257.82027

Summary: The problem of enumerating close-packed dimers, or perfect matchings, on two types of lattices (the so-called 8.8.4 and 8.8.6 lattices) embedded on the Klein bottle is considered, and we obtain the explicit expression of the number of close-packed dimers and entropy. Our results imply that 8.8.4 lattices have the same entropy under three different boundary conditions (cylindrical, toroidal and Klein bottle) and 8.8.6 lattices have the same property.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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