Can I read The number of Z-convex polyominoes on EtoBox?

The number of Z-convex polyominoes by Enrica Duchi; Simone Rinaldi; Gilles Schaeffer is a Mathematics article available to read on EtoBox.

What is The number of Z-convex polyominoes about?

In this paper we consider a restricted class of 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). This class of convex polyominoes appears to resist standard decompositions, so 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.

Who reads The number of Z-convex polyominoes?

Author

Enrica Duchi; Simone Rinaldi; Gilles Schaeffer

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0196-8858)

Published

2008

Language

EN

Field

Mathematics (Physical Sciences)