A Partition-Based Generating Function for Row-Convex Polyominoes
An alternative generating function is proposed to enumerate row-convex polyominoes without internal holes on a discrete grid. The approach is based on integer partitions of the total area, where each partition corresponds to a sequence of row lengths, and the product of all permutations of the parts accounts for all possible horizontal alignments of consecutive rows. Summing over the products yields a formula for the total number of convex polyominoes of a given size. Numerical examples are provided for small areas, and the exact generating function is derived via a transfer series argument, establishing the asymptotic growth S(N) as A2^(N) cos(N*theta) + phi) with theta = arctan(sqrt(7)/...
| Authors | Vincenzo M. Scarrica |
|---|---|
| Primary category | math.CO |
| Published | 4 May 2026 |
| Last updated at source | 4 May 2026 |
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