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

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DMTCS Conference vol AE (2005), pp. 369-374


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

Stefan Felsner (ed.)

DMTCS Conference Volume AE (2005), pp. 369-374

author: Gill Barequet, Micha Moffie, Ares Ribó and Günter Rote
title: Counting Polyominoes on Twisted Cylinders
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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reference: Gill Barequet and Micha Moffie and Ares Ribó and Günter Rote (2005), Counting Polyominoes on Twisted Cylinders, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 369-374
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