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The generating function of convex polyominoes: The resolution of a q-differential system

✍ Scribed by Mireille Bousquet-Mélou; Jean-Marc Fédou

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
825 KB
Volume
137
Category
Article
ISSN
0012-365X

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✦ Synopsis

We give a 'beautiful' though complex -formula for the generating function Z of convex polyominoes, according to their area, width and height. Our method consists in solving a linear q-differential system of size three, which was derived two years ago by encoding convex polyominoes with the words of an algebraic language (Schfitzenberger's methodology). Three other formulas had already been obtained for Z, but neither was entirely satisfying.

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Enumeration of Symmetry Classes of Conve
Enumeration of Symmetry Classes of Convex Polyominoes in the Square Lattice
✍ P. Leroux; E. Rassart; A. Robitaille 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 544 KB

This paper concerns the enumeration of rotation-type and congruence-type convex polyominoes on the square lattice. These can be defined as orbits of the Ž groups ᑝ , of rotations, and ᑞ , of symmetries, of the square, acting on transla-4 4 . tion-type polyominoes. By virtue of Burnside's lemma, it i