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On the Tiling System Recognizability of Various Classes of Convex Polyominoes
F. De Carli1, A. Frosini1, S. Rinaldi1, and L. Vuillon2
1Dipartimento di Scienze Matematiche e Informatiche, Universit\`a di Siena, Pian dei Mantellini, 44 53100, Siena, Italy
{frosini, rinaldi}@unisi.it
2Laboratoire de Math\'ematiques, UMR 5127 CNRS, Universit\'e de Savoie, 73376 Le Bourget du Lac, France
Laurent.Vuillon@univ-savoie.fr
Annals of Combinatorics 13 (2) pp.169-191 June, 2009
AMS Subject Classification: 52C45, 68R15, 68R05
Abstract:
We consider some problems concerning two relevant classes of two-dimensional languages, i.e., the {\em tiling recognizable languages}, and the {\em local languages}, recently introduced by Giammarresi and Restivo and already extensively studied. We show that various classes of convex and column-convex polyominoes can be naturally represented as two-dimensional words of tiling recognizable languages. Moreover, we investigate the nature of the generating function of a tiling recognizable language, providing evidence that such a generating function need not be D-finite.
Keywords: convex polyominoes, two-dimensional languages, tiling systems, generating functions

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