Auspicious Tatami Mat Arrangements

  title={Auspicious Tatami Mat Arrangements},
  author={Alejandro Erickson and Frank Ruskey and Mark Schurch and Jennifer Woodcock},
We introduce tatami tilings, and present some of the many interesting questions that arise when studying them. Roughly speaking, we are considering 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… 
Teaching the art of computer programming (TAOCP)
The author's experience in teaching two courses, each based on different sections of TAOCP volume 4a, using the pre-fascicles and fascicles that were available at the time can be extremely rewarding, not only for the students, but also for the instructor.


Counting Fixed-Height Tatami Tilings
This work presents and uses 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 $n \ge m$ and uses it to verify a modified version of a conjecture of Knuth.
On tiling under tomographic constraints
In this note, progress is made toward a comprehensive classification of various tiling reconstruction problems, by proving NP-completeness results for several sets of tiles.
A Note on Tatami Tilings
Inspired by the rules of Japanese tatami layouts, we present in these paper some characteriza- tion results of tiling rectangles with 1x2 and 2x1 blocks in case a single 1x1 block is allowed. The
On dimer coverings of rectangles of fixed width
  • R. Stanley
  • Computer Science, Mathematics
    Discret. Appl. Math.
  • 1985
Various properties of the generating function ]~ An xn are obtained, in particular answering questions of Klarner and Pollack and of Hock and McQuistan, and an explicit expression for the molecular freedom for dimers on a saturated k × n lattice space is obtained.
Combinatorial Approaches and Conjectures for 2-Divisibility Problems Concerning Domino Tilings of Polyominoes
  • L. Pachter
  • Mathematics, Computer Science
    Electron. J. Comb.
  • 1997
We give the first complete combinatorial proof of the fact that the number of domino tilings of the 2n×2n square grid is of the form 2^n(2k + 1)^2, thus settling a question raised by John, Sachs, and
Reconstructing 3-Colored Grids from Horizontal and Vertical Projections Is NP-hard
The problem of coloring a grid using k colors with the restriction that in each row and each column has an specific number of cells of each color is considered, and it is shown that for 3 colors the problem is already NP-hard.
A Reciprocity Theorem for Monomer-Dimer Coverings
It is shown that M(m,n), a priori a rational number, is always an integer, using a generalization of the combinatorial model offered by Propp, which was applicable to higher-dimensional cases.
The Art of Computer Programming, Volume 4, Fascicle 2: Generating All Tuples and Permutations (Art of Computer Programming)
Volume 4, Fascicle 4This latest fascicle covers the generation of all trees, a basic topic that has surprisingly rich ties to the first three volumes of The Art of Computer Programming, and continues to build a firm foundation for programming.
Ramanujan's method in q-series congruences
We show that the method that was developed by Ramanujan to prove $5|p (5n + 4)$ and $7|p (7n + 5)$ may, in fact, be extended to a wide variety of $q$-series and products including some with free
On a Problem of Marco Buratti
This work considers a problem formulated by Marco Buratti concerning Hamiltonian paths in the complete graph on Z_p, an odd prime, and its application to graph analysis.