Auspicious Tatami Mat Arrangements

The main purpose of this paper is to introduce the idea of tatami tilings, and to present some of the many interesting and fun questions that arise when studying them. Roughly speaking, we are considering are tilings of rectilinear regions with 1×2 dimer tiles and 1×1 monomer tiles, with the constraint that no four corners of the tiles meet. Typical problems are to minimize the number of monomers in a tiling, or to count the number of tilings in a particular shape. We determine the underlying structure of tatami tilings of rectangles and use this to prove that the number of tatami tilings of an n × n square with n monomers is n2n−1 . We also prove that, for fixed-height, the number of tatami tilings of a rectangle is a rational function and outline an algorithm that produces the coefficients of the two polynomials of the numerator and the denominator. Many interesting and fun open problems remain to be solved.

• Type: Conference
• Year: 2010
• Where: COCOON
• Authors: Alejandro Erickson, Frank Ruskey, Mark Schurch, Jennifer Woodcock
• Keywords: COCOON 2010, Combinatorics, Monomer Tiles, Monomers, Tatami Tilings