Exhaustive generation of gominoes

Authors:
Jérôme Fortier;Alain Goupil;Jonathan Lortie;Jérôme Tremblay
Affiliations:
LaCIM, Université du Québec í Montréal, C. P. 8888 Succursale "Centre-Ville", Montréal (QC), H3C 3P8, Canada;Département de mathématiques et d'informatique, Université du Québec í Trois-Rivières, 3351 boul. des Forges, C.P. 500, Trois-Rivières (QC), G9A 5H7, Canada;LaCIM, Université du Québec í Montréal, C. P. 8888 Succursale "Centre-Ville", Montréal (QC), H3C 3P8, Canada;LaCIM, Université du Québec í Montréal, C. P. 8888 Succursale "Centre-Ville", Montréal (QC), H3C 3P8, Canada
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

In this paper, we consider the generation of three classes of polyominoes, distinguished by their connectivity type. We present a two-player game called gomino, and we show how this game induces an algorithm to generate these sets of polyominoes according to their site-perimeter. We then use a variation of the gomino algorithm to obtain exact expressions for the number of polyominoes inscribed in a rectangle of size bxk with area bk-r, where r@?5.