Enumeration of convex polyominoes using the ECO method

Abstract : ECO is a method for the enumeration of classes of combinatorial objects based on recursive constructions of such classes. In the first part of this paper we present a construction for the class of convex polyominoes based on the ECO method. Then we translate this construction into a succession rule. The final goal of the paper is to determine the generating function of convex polyominoes according to the semi-perimeter, and it is achieved by applying an idea introduced in [11].
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Michel Morvan and Éric Rémila. Discrete Models for Complex Systems, DMCS'03, 2003, Lyon, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03), pp.103-116, 2003, DMTCS Proceedings
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A. Del Lungo, E. Duchi, A. Frosini, S. Rinaldi. Enumeration of convex polyominoes using the ECO method. Michel Morvan and Éric Rémila. Discrete Models for Complex Systems, DMCS'03, 2003, Lyon, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03), pp.103-116, 2003, DMTCS Proceedings. 〈hal-01183315〉

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