ON THE AREA OF SQUARE LATTICE POLYGONS

被引：31

作者：

ENTING, IG ^{[1
]}

GUTTMANN, AJ ^{[1
]}

机构：

[1] UNIV MELBOURNE,DEPT MATH,PARKVILLE,VIC 3052,AUSTRALIA

来源：

JOURNAL OF STATISTICAL PHYSICS | 1990年 / 58卷 / 3-4期

关键词：

Square lattice polygons;

D O I：

10.1007/BF01112757

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the generating function of self-avoiding square lattice polygons grouped by both area and perimeter. The generating function for polygons of area n is found to diverge at xc=0.251834, with an exponent of zero. The mean perimeter of polygons with area n is found to be proportional to n, while the mean area of polygons with perimeter n is found to be proportional to n1.5. © 1990 Plenum Publishing Corporation.

引用

页码：475 / 484

页数：10

共 19 条

[1]

[Anonymous], 1989, PHASE TRANSITIONS CR

[2]

BENDER E, 1974, DISCRETE MATH, V8, P219

[3]

Brak R., UNPUB

[4] ALGEBRAIC LANGUAGES AND POLYOMINOES ENUMERATION [J].

DELEST, MP ;

VIENNOT, G .

THEORETICAL COMPUTER SCIENCE, 1984, 34 (1-2) :169-206

[5] GENERATING-FUNCTIONS FOR ENUMERATING SELF-AVOIDING RINGS ON THE SQUARE LATTICE [J].

ENTING, IG .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1980, 13 (12) :3713-3722

[6] POLYGONS ON THE HONEYCOMB LATTICE [J].

ENTING, IG ;

GUTTMANN, AJ .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1989, 22 (09) :1371-1384

[7]

ENTING IG, IN PRESS J PHYS A, V2

[8] 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

[9] ON THE CRITICAL-BEHAVIOR OF SELF-AVOIDING WALKS [J].

GUTTMANN, AJ .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1987, 20 (07) :1839-1854

[10] 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

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