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Ferrers Graph Polygon

FerrersGraphPolygon

A Ferrers graph polygon is a self-avoiding polygon containing three corners of its minimal bounding rectangle. The anisotropic area and perimeter generating function G(x,y) and partial generating functions H_m(y), connected by

G(x,y,q)=sum_(m>=1)H_m(y,q)x^m,
(1)

satisfy the self-reciprocity and inversion relations

H_m(1/y,1/q)=(-1)^my^(m-2)q^((m^3-3m)/2)H_m(y,q)
(2)

and

G(x,y)-y^2G(-x/y,1/y)=0
(3)

(Bousquet-Mélou et al. 1999).

See also

Lattice Polygon, Self-Avoiding Polygon

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References

Bousquet-Mélou, M.; Guttmann, A. J.; Orrick, W. P.; and Rechnitzer, A. "Inversion Relations, Reciprocity and Polyominoes." 23 Aug 1999. https://arxiv.org/abs/math/9908123.

Referenced on Wolfram|Alpha

Ferrers Graph Polygon

Cite this as:

Weisstein, Eric W. "Ferrers Graph Polygon." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FerrersGraphPolygon.html

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