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{\bf Alejandro Erickson, Frank Ruskey, Jennifer Woodcock and Mark Schurch}
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{\bf Monomer-Dimer Tatami Tilings of Rectangular Regions}
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In this paper we consider tilings of rectangular regions with two
types of tiles, $1 \times 2$ tiles (dimers) and $1 \times 1$ tiles
(monomers). The tiles must cover the region and satisfy the
constraint that no four corners of the tiles meet; such tilings are
called \emph{tatami tilings}. We provide a structural
characterization and use it to prove that the tiling is completely
determined by the tiles that are on its border. We prove that the
number of tatami tilings of an $n \times n$ square with $n$ monomers
is $n2^{n-1}$. We also show that, for fixed-height, the generating
function for the number of tatami tilings of a rectangle is a rational
function, and outline an algorithm that produces the generating
function.
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