Combinatorial approaches and conjectures for 2-divisibility problems concerning domino tilings of polyominoes (Q1378522)

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.