A tatami tiling is an arrangement of 1 Ã— 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 useâ€¦ (More)

In this paper we consider tilings of rectangular regions with two types of tiles, 1Ã— 2 tiles (dimers) and 1Ã— 1 tiles (monomers). The tiles must cover the region and satisfy the constraint that noâ€¦ (More)

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 areâ€¦ (More)

We outline the progress made so far on the search for the complete set of torus obstructions and also consider practical algorithms for torus embedding and their implementations. We present the setâ€¦ (More)

The Rand distances of two set partitions is the number of pairs {x, y} such that there is a block in one partition containing both x and y, but x and y are in different blocks in the other partition.â€¦ (More)