Tilings by Translation: Enumeration by a Rational Language Approach

Author:

Brlek Srecko,Frosini Andrea,Rinaldi Simone,Vuillon Laurent

Abstract

Beauquier and Nivat introduced and gave a characterization of the class of pseudo-square polyominoes, i.e. those polyominoes that tile the plane by translation: a polyomino tiles the plane by translation if and only if its boundary word $W$ may be factorized as $W = XY\overline{X} \,\overline{Y}$. In this paper we consider the subclass PSP of pseudo-square polyominoes which are also parallelogram. By using the Beauquier-Nivat characterization we provide by means of a rational language the enumeration of the subclass of $psp$-polyominoes with a fixed planar basis according to the semi-perimeter. The case of pseudo-square convex polyominoes is also analyzed.

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the Arithmetics of Discrete Figures;Language and Automata Theory and Applications;2014

2. On the shape of permutomino tiles;Discrete Applied Mathematics;2013-10

3. Exhaustive generation of gominoes;Theoretical Computer Science;2013-09

4. A decomposition theorem for homogeneous sets with respect to diamond probes;Computer Vision and Image Understanding;2013-04

5. Tiling the Plane with Permutations;Discrete Geometry for Computer Imagery;2011

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