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The Number of Convex Polyominoes and the Generating Function of Jacobi Polynomials

Victor J. W. Guo·Jiang Zeng
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Abstract

Lin and Chang gave a generating function of convex polyominoes with an $m+1$ by $n+1$ minimal bounding rectangle. Gessel showed that their result implies that the number of such polyominoes is $$ \frac{m+n+mn}{m+n}{2m+2n\choose 2m}-\frac{2mn}{m+n}{m+n\choose m}^2. $$ We show that this result can be derived from some binomial coefficients identities related to the generating function of Jacobi polynomials.

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Victor J. W. Guo, Jiang Zeng. 2004-03-24. The Number of Convex Polyominoes and the Generating Function of Jacobi Polynomials. https://arxiv.org/abs/math/0403262

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