| Issue |
RAIRO-Theor. Inf. Appl.
Volume 59, 2025
Generation, enumeration and tiling
|
|
|---|---|---|
| Article Number | 11 | |
| Number of page(s) | 22 | |
| DOI | https://doi.org/10.1051/ita/2025011 | |
| Published online | 15 October 2025 | |
Efficient counting of k-convex polyominoes
1
School of Mathematics and Statistics, The University of Melbourne, Australia
2
Department of Theoretical and Applied Sciences, University of Insubria, Italy
* Corresponding author: paolo.massazza@uninsubria.it
Received:
2
March
2025
Accepted:
6
September
2025
The degree of convexity of a convex polyomino P is the smallest integer k such that any two cells of P can be joined by a monotone path inside P with at most k changes of direction. In this paper, we show that, for any fixed integer k > 2, the number of polyominoes of area n and degree of convexity at most k can be computed in polynomial time using O(n4) space.
Mathematics Subject Classification: 05B50 / 05A15
Key words: Convex polyominoes / counting problem / integer sequences
© The authors. Published by EDP Sciences, 2025
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