A stack polyomino is a self-avoiding convex polyomino containing two adjacent corners of its minimal bounding rectangle. The number of stack polyominoes with perimeter is the Fibonacci number , having generating function
(1)
(Delest and Viennot 1984).
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 alsoConvex Polyomino,
Lattice Polygon,
Self-Avoiding Polygon Explore with Wolfram|Alpha ReferencesBousquet-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.Delest, M.-P. and Viennot, G. "Algebraic Languages and Polyominoes [sic] Enumeration." Theoret. Comput. Sci. 34, 169-206, 1984.Wright, E. M. "Stacks." Quart. J. Math. (Oxford) 19, 313-320, 1968. Referenced on Wolfram|AlphaStack Polyomino Cite this as:Weisstein, Eric W. "Stack Polyomino." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StackPolyomino.html
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