Gill Barequet, Micha Moffie, Ares Ribó, and Günter Rote:

Counting polyominoes on twisted cylinders

  1. Discrete Mathematics and Theoretical Computer Science AE (2005), 369-374.
  2. INTEGERS: The Electronic Journal of Combinatorial Number Theory 6 (2006), article #A22, 37 pages.

Abstract

Using numerical methods, we analyze the growth in the number of polyominoes on a twisted cylinder as the number of cells increases. These polyominoes are related to classical polyominoes (connected subsets of a square grid) that lie in the plane. We thus obtain an improved lower bound of 3.980137 on the growth rate of the number of polyominoes, which is also known as Klarner's constant. We use a dynamic programming approach. For storing information about partial polyominos, we make use of a bijection between "states" of our system and Motzkin paths.
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Last update: May 14, 2008.