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Pré-Publication, Document De Travail Année : 2006

The number of Z-convex polyominoes

Résumé

In this paper we consider a restricted class of convex polyominoes that we call Z-convex polyominoes. Z-convex polyominoes are polyominoes such that any two pairs of cells can be connected by a monotone path making at most two turns (like the letter Z). In particular they are convex polyominoes, but they appear to resist standard decompositions. We propose a construction by ``inflation'' that allows to write a system of functional equations for their generating functions. The generating function P(t) of Z-convex polyominoes with respect to the semi-perimeter turns out to be algebraic all the same and surprisingly, like the generating function of convex polyominoes, it can be expressed as a rational function of t and the generating function of Catalan numbers.

Dates et versions

hal-00019885 , version 1 (28-02-2006)

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Citer

Enrica Duchi, Simone Rinaldi, Gilles Schaeffer. The number of Z-convex polyominoes. 2006. ⟨hal-00019885⟩
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