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Parallelogram Polyomino

A parallelogram polyomino is a polyomino such that the intersection with every line perpendicular to the main diagonal is a connected segment. The number of parallelogram polyominoes with perimeter 2n+2 is the Catalan number

C_n=1/(n+1)(2n; n),

where (n; k) is a binomial coefficient (Delest and Viennot 1984).

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References

Delest, M.-P. and Viennot, G. "Algebraic Languages and Polyominoes [sic] Enumeration." Theoret. Comput. Sci. 34, 169-206, 1984.Fürlinger, J. and Hofbauer, J. "q-Catalan Numbers." J. Combin. Th. Ser. A 40, 248-264, 1985.Gessel, J. "A Noncommutative Generalization and q-Analog of the Lagrange Inversion Formula." Trans. Amer. Math. Soc. 257, 455-482, 1980.Pólya, G. "On the Number of Certain Lattice Polygons." J. Combin. Th. 6, 102-105, 1969.

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Parallelogram Polyomino

Cite this as:

Weisstein, Eric W. "Parallelogram Polyomino." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ParallelogramPolyomino.html

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