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Combinatorial approaches and conjectures for 2-divisibility problems concerning domino tilings of polyominoes. (English) Zbl 0886.05046

Electron. J. Comb. 4, No. 1, Research paper R29, 10 p. (1997); printed version J. Comb. 4, No. 1, 401-410 (1997).
Summary: We give the first complete combinatorial proof of the fact that the number of domino tilings of the \(2n\times 2n\) square grid is of the form \(2^n(2k+ 1)^2\). The proof lends itself naturally to some interesting generalizations, and leads to a number of new conjectures.

MSC:

05B45 Combinatorial aspects of tessellation and tiling problems
05B50 Polyominoes