Enumeration of L-convex polyominoes by rows and columns

Authors:
G. Castiglione;A. Frosini;A. Restivo;S. Rinaldi
Affiliations:
Dipartimento di Matematica e Applicazioni, Università di Palermo, Palermo, Italy;Dipartimento di Scienze Matematiche ed Informatiche, Università di Siena, Pian dei Mantellini, Siena, Italy;Dipartimento di Matematica e Applicazioni, Università di Palermo, Palermo, Italy;Dipartimento di Scienze Matematiche ed Informatiche, Università di Siena, Pian dei Mantellini, Siena, Italy
Venue:
Theoretical Computer Science
Year:
2005

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Abstract

In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once.Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the rational recurrence relation fn = 4fn-1 - 2fn-2, with f0 = 1, f1 = 2, f2 = 7. Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.