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].

Keywords

• convex polyominoes
• eco method
• succession rules
• kernel method
• generating functions
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [nlin.nlin-cg] nonlinear sciences [physics]/cellular automata and lattice gases [nlin.cg]