Pachter, Lior 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. Cited in 13 Documents MSC: 05B45 Combinatorial aspects of tessellation and tiling problems 05B50 Polyominoes Keywords:domino tilings; square grid × Cite Format Result Cite Review PDF Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: Number of domino tilings (or dimer coverings) of a 2n X 2n square. Array T(m,n) read by antidiagonals: number of domino tilings (or dimer tilings) of the m X n grid (or m X n rectangle), for m>=1, n>=1.