@inproceedings{72c850765d454ac184a1d1a9fc50426f,
title = "Formulae for polyominoes on twisted cylinders",
abstract = "Polyominoes are edge-connected sets of cells on the square lattice ℤ2. We investigate polyominoes on a square lattice embedded on so-called twisted cylinders of a bounded width (perimeter) w. We prove that the limit growth rate of polyominoes of the latter type approaches that of polyominoes of the former type, as w tends to infinity. We also prove that for any fixed value of w, the formula enumerating polyominoes on a twisted cylinder of width w satisfies a linear recurrence whose complexity grows exponentially with w. By building the finite automaton that {"}grows{"} polyominoes on the twisted cylinder, we obtain the prefix of the sequence enumerating these polyominoes. Then, we recover the recurrence formula by using the Berlekamp-Massey algorithm.",
keywords = "Recurrence formula, generating function, transfer matrix",
author = "Gadi Aleksandrowicz and Andrei Asinowski and Gill Barequet and Ronnie Barequet",
year = "2014",
doi = "10.1007/978-3-319-04921-2_6",
language = "الإنجليزيّة",
isbn = "9783319049205",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "76--87",
booktitle = "Language and Automata Theory and Applications - 8th International Conference, LATA 2014, Proceedings",
note = "8th International Conference on Language and Automata Theory and Applications, LATA 2014 ; Conference date: 10-03-2014 Through 14-03-2014",
}