Author:
Ruskey Frank,Woodcock Jennifer
Abstract
A tatami tiling is an arrangement of $1 \times 2$ dominoes (or mats) in a rectangle with $m$ rows and $n$ columns, subject to the constraint that no four corners meet at a point. For fixed $m$ we present and use Dean Hickerson's combinatorial decomposition of the set of tatami tilings — a decomposition that allows them to be viewed as certain classes of restricted compositions when $n \ge m$. Using this decomposition we find the ordinary generating functions of both unrestricted and inequivalent tatami tilings that fit in a rectangle with $m$ rows and $n$ columns, for fixed $m$ and $n \ge m$. This allows us to verify a modified version of a conjecture of Knuth. Finally, we give explicit solutions for the count of tatami tilings, in the form of sums of binomial coefficients.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
5 articles.
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1. Monte Carlo estimation of the number of tatami tilings;International Journal of Modern Physics C;2016-08-29
2. Domino Tatami Covering Is NP-Complete;Lecture Notes in Computer Science;2013
3. Monomer-dimer tatami tilings of square regions;Journal of Discrete Algorithms;2012-10
4. Enumerating Tatami Mat Arrangements of Square Grids;Lecture Notes in Computer Science;2011
5. Auspicious Tatami Mat Arrangements;Lecture Notes in Computer Science;2010