A column-convex self-avoiding polygon which contains the bottom edge of its minimal bounding rectangle. The anisotropic perimeter and area generating function
(1)
where is the number of polygons with horizonal bonds, vertical bonds, and area , has been computed exactly for the bar graph polygons (Bousquet-Mélou 1996, Bousquet-Mélou et al. 1999). The anisotropic area and perimeter generating function and partial generating functions , connected by
(2)
satisfy the self-reciprocity and inversion relations
(3)
and
(4)
(Bousquet-Mélou et al. 1999).
See alsoLattice Polygon,
Self-Avoiding Polygon Explore with Wolfram|Alpha ReferencesBousquet-Mélou, M. "A Method for Enumeration of Various Classes of Column-Convex Polygons." Disc. Math. 154, 1-25, 1996.Bousquet-Mélou, M.; Guttmann, A. J.; Orrick, W. P.; and Rechnitzer, A. "Inversion Relations, Reciprocity and Polyominoes." 23 Aug 1999. http://arxiv.org/abs/math.CO/9908123. Referenced on Wolfram|AlphaBar Graph Polygon Cite this as:Weisstein, Eric W. "Bar Graph Polygon." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BarGraphPolygon.html
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