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

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dc.creatorGuo, Victor J. W.
dc.creatorZeng, Jiang
dc.date2004-03-16
dc.date2004-03-24
dc.date.accessioned2026-07-07T05:06:27Z
dc.date.available2026-07-07T05:06:27Z
dc.descriptionLin 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.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0403262
dc.identifierhttp://arxiv.org/abs/math/0403262
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70475
dc.subjectCombinatorics
dc.subject05A15, 05A19
dc.titleThe Number of Convex Polyominoes and the Generating Function of Jacobi Polynomials
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