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<p>A <i>polyomino</i> is an edge-connected set of squares on the square lattice. In this paper, we improve the Conway-Jensen polyomino-counting algorithm by considering bounding boxes on the square lattice rotated by&#xa0;<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(45^\circ \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>45</mn> <mo>∘</mo> </msup> </math></EquationSource> </InlineEquation> instead of on the regular unrotated lattice. This allows us to extend significantly the count of polyominoes from&#xa0;56 to&#xa0;70 terms.</p>

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Counting Polyominoes, Revisited

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Gill Barequet,
  • Gil Ben-Shachar

摘要

A polyomino is an edge-connected set of squares on the square lattice. In this paper, we improve the Conway-Jensen polyomino-counting algorithm by considering bounding boxes on the square lattice rotated by  \(45^\circ \) 45 ∘ instead of on the regular unrotated lattice. This allows us to extend significantly the count of polyominoes from 56 to 70 terms.