THE GENERATING FUNCTION OF CONVEX POLYOMINOES - THE RESOLUTION OF A Q-DIFFERENTIAL SYSTEM

被引：21

作者：

BOUSQUETMELOU, M ^{[1
]}

FEDOU, JM ^{[1
]}

机构：

[1] UNIV BORDEAUX 1,LABRI,F-33505 TALENCE,FRANCE

来源：

DISCRETE MATHEMATICS | 1995年 / 137卷 / 1-3期

关键词：

D O I：

10.1016/0012-365X(93)E0161-V

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 (Schutzenberger's methodology). Three other formulas had already been obtained for Z, but neither was entirely satisfying.

引用

页码：53 / 75

页数：23

共 14 条

[1]

ANDREWS GE, 1976, ENCY MATH ITS APPLIC, V2

[2]

BENDER E, 1974, DISCRETE MATH, V8, P219

[3] HEAPS OF SEGMENTS AND Q-ENUMERATION OF DIRECTED CONVEX POLYOMINOES [J].