Geodesic
Counting Polyominoes on Twisted Cylinders
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005).

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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. 
@article{DMTCS_2005_special_250_a55,
     author = {Barequet, Gill and Moffie, Micha and Rib\'o, Ares and Rote, G\"unter},
     title = {Counting {Polyominoes} on {Twisted} {Cylinders}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)},
     year = {2005},
     doi = {10.46298/dmtcs.3446},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3446/}
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Barequet, Gill; Moffie, Micha; Ribó, Ares; Rote, Günter. Counting Polyominoes on Twisted Cylinders. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005). doi : 10.46298/dmtcs.3446. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3446/

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