EXACT SOLUTION OF THE STAIRCASE AND ROW-CONVEX POLYGON PERIMETER AND AREA GENERATING FUNCTION

被引：47

作者：

BRAK, R

GUTTMANN, AJ

机构：

[1] Dept. of Math., Melbourne Univ., Parkville, Vic.

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1990年 / 23卷 / 20期

关键词：

D O I：

10.1088/0305-4470/23/20/019

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

An explicit expression is obtained for the perimeter and area generating function G(y, z)= Sigma n>or=2 Sigma m>or=1 c n,mynZm, where cn,m is the number of row-convex polygons with area m and perimeter n. A similar expression is obtained for the area-perimeter generating function for staircase polygons. Both expressions contain q-series.

引用

收藏

页码：4581 / 4588

页数：8

相关论文

共 12 条

[1] EXACT SOLUTION OF THE ROW-CONVEX POLYGON PERIMETER GENERATING FUNCTION [J].

BRAK, R ;

GUTTMANN, AJ ;

ENTING, IG .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (12) :2319-2326

[2]

DELEST MP, 1984, THEOR COMPUT SCI, V34, P3377

[3]

ENTING IG, 1980, J PHYS A, V22, P2639

[4] THE NUMBER OF CONVEX POLYGONS ON THE SQUARE AND HONEYCOMB LATTICES [J].

GUTTMANN, AJ ;

ENTING, IG .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1988, 21 (08) :L467-L474

[5] THE SIZE AND NUMBER OF RINGS ON THE SQUARE LATTICE [J].

GUTTMANN, AJ ;

ENTING, IG .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1988, 21 (03) :L165-L172

[6] THE NUMBER OF CONVEX POLYOMINOS WITH GIVEN PERIMETER [J].

KIM, D .

DISCRETE MATHEMATICS, 1988, 70 (01) :47-51

[7] RIGOROUS RESULTS FOR THE NUMBER OF CONVEX POLYGONS ON THE SQUARE AND HONEYCOMB LATTICES [J].

LIN, KY ;

CHANG, SJ .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1988, 21 (11) :2635-2642

[8]

LIN KY, 1990, PREPRINT NAWTIONAL T

[9]

Polya G, 1969, J COMB THEORY, V6, P102

[10] DIFFERENCE-EQUATIONS IN STATISTICAL-MECHANICS .1. CLUSTER STATISTICS MODELS [J].

PRIVMAN, V ;

SVRAKIC, NM .

JOURNAL OF STATISTICAL PHYSICS, 1988, 51 (5-6) :1091-1110