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October 17, 2025RAIRO - Theoretical Informatics and Applications0 citationsOpen Access

Efficient counting of k-convex polyominoes

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AGA J GuttmannPMPaolo Massazza

Key Points

  • The number of k-convex polyominoes can be efficiently counted based on the area.
  • The proposed method operates in polynomial time with a space complexity of O(n^4).
  • The approach focuses on the degree of convexity, highlighting changes of direction in the structure.
  • This work extends counting techniques for convex polyominoes, providing new insights into combinatorial geometry.

Abstract

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 ( n 4 ) space.

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Cite This Study

Guttmann et al. (2025) studied this question.

synapsesocial.com/papers/68f199bfde32064e504dc9a7https://doi.org/10.1051/ita/2025011
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  5. 5A method for the enumeration of various classes of column-convex polygons1996 · 238 citations