The number of Z-convex polyominoes
| dc.creator | Duchi, Enrica | |
| dc.creator | Rinaldi, Simone | |
| dc.creator | Schaeffer, Gilles | |
| dc.date | 2006-02-07 | |
| dc.date.accessioned | 2026-07-07T07:03:10Z | |
| dc.date.available | 2026-07-07T07:03:10Z | |
| dc.description | 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. | |
| dc.description | 15 pages, 14 figures | |
| dc.identifier | https://arxiv.org/abs/math/0602124 | |
| dc.identifier | http://arxiv.org/abs/math/0602124 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108873 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 | |
| dc.title | The number of Z-convex polyominoes | |
| dc.type | text |