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

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

2004-03-16

arxiv.org/abs/math/0403262v2

Mathematics

Combinatorics

8 pages

Scientific paper

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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