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Counting Polyominoes on Twisted Cylinders
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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 $\textit{twisted cylinder}$ 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.
Centre pour la Communication Scientifique Directe (CCSD)
Title: Counting Polyominoes on Twisted Cylinders
Description:
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 $\textit{twisted cylinder}$ 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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