Exact solution of the convex polygon perimeter and area generating function
K Y Lin; K Y Lin; Dept. of Phys. Nat. Tsing Hua Univ., Hsinchu, Taiwan
Журнал:
Journal of Physics A: Mathematical and General
Дата:
1991-05-21
Аннотация:
An explicit expression is derived for the three-variable generating function P(x, y, z)= Sigma <sub>m>or=1</sub>, Sigma <sub>n</sub>>or=<sub>1</sub> Sigma <sub>r</sub>>or=<sub>1</sub> x<sup>2n</sup>y<sup>2m</sup>z<sup>r</sup>c<sub>n,m,r</sub>, where c<sub>n,m,r</sub> is the number of convex polygons with horizontal width n, vertical height m and area r.
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