DMTCS Proceedings, 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

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Counting Polyominoes on Twisted Cylinders

Gill Barequet, Micha Moffie, Ares Ribó, Günter Rote


We improve the lower bounds on Klarner's constant, which describes the exponential growth rate of the number of polyominoes (connected subsets of grid squares) with a given number of squares. We achieve this by analyzing polyominoes on a different surface, a so-called twisted cylinder by the transfer matrix method. A bijective representation of the ``states'' of partial solutions is crucial for allowing a compact representation of the successive iteration vectors for the transfer matrix method.

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