Counting Polyominoes on Twisted Cylinders
Gill Barequet, Micha Moffie, Ares Ribó, Günter Rote
Abstract
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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