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{\bf Lior Pachter}\medskip\noindent
{\bf Combinatorial Approaches and Conjectures for 
2-Divisibility Problems Concerning Domino Tilings of
 Polyominoes}
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 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 $2^n(2k+1)^2$, 
thus settling a question raised by John, Sachs, and 
Zernitz.
 The proof lends itself
naturally to some interesting generalizations, and leads to a number of 
new conjectures.
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