On the Tiling System Recognizability of Various Classes of Convex Polyominoes |
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Authors: | F De Carli A Frosini S Rinaldi L Vuillon |
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Institution: | 1. Dipartimento di Scienze Matematiche e Informatiche, Università di Siena, Pian dei Mantellini, 44 53100, Siena, Italy 2. Laboratoire de Mathématiques, UMR 5127 CNRS, Université de Savoie, 73376, Le Bourget du Lac, France
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Abstract: | We consider some problems concerning two relevant classes of two-dimensional languages, i.e., the tiling recognizable languages, and the 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. |
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