EXACT SOLUTION OF THE CONVEX POLYGON PERIMETER AND AREA GENERATING FUNCTION

An explicit expression is derived for the three-variable generating function P(x, y, z)= Sigma m>or=1, Sigma n>or=1 Sigma r>or=1 x2ny2mzrcn,m,r, where cn,m,r is the number of convex polygons with horizontal width n, vertical height m and area r.

[1]  Anthony J. Guttmann,et al.  Area-weighted moments of convex polygons on the square lattice , 1989 .

[2]  K. Lin,et al.  Rigorous results for the number of convex polygons on the square and honeycomb lattices , 1988 .

[3]  Anthony J. Guttmann,et al.  The number of convex polygons on the square and honeycomb lattices , 1988 .

[4]  P. Gennes.  Scaling Concepts in Polymer Physics , 1979 .

[5]  A. Guttmann,et al.  Exact solution of the staircase and row-convex polygon perimeter and area generating function , 1990 .

[6]  A. C. Hearn,et al.  REDUCE: a user-oriented interactive system for algebraic simplification , 1967, Symposium on Interactive Systems for Experimental Applied Mathematics.

[7]  Number of anisotropic spiral self-avoiding loops , 1987 .

[8]  V. Privman,et al.  Difference equations in statistical mechanics. I. Cluster statistics models , 1988 .

[9]  George Polya,et al.  On the number of certain lattice polygons , 1969 .

[10]  K. Lin.  Perimeter generating function for row-convex polygons on the rectangular lattice , 1990 .

[11]  H. Temperley.  Combinatorial Problems Suggested by the Statistical Mechanics of Domains and of Rubber-Like Molecules , 1956 .

[12]  Dongsu Kim,et al.  The number of convex polyominos with given perimeter , 1988, Discret. Math..

[13]  Anthony J. Guttmann,et al.  Exact solution of the row-convex polygon perimeter generating function , 1990 .

[14]  G. Andrews.  The Theory of Partitions: Frontmatter , 1976 .

[15]  H. Temperley.  Statistical mechanics and the partition of numbers II. The form of crystal surfaces , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  Gérard Viennot,et al.  Algebraic Languages and Polyominoes Enumeration , 1983, Theor. Comput. Sci..