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<p>We present algorithms for classifying rational polygons with fixed denominator and number of interior lattice points. Our approach is to first describe maximal polygons and then compute all subpolygons, where we eliminate redundancy by a suitable normal form. Executing our classification, we obtained a dataset of several billions of polygons covering a wide variety of cases.</p>

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Classifying Rational Polygons with Small Denominator and Few Interior Lattice Points

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月7日

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  • Martin Bohnert,
  • Justus Springer

摘要

We present algorithms for classifying rational polygons with fixed denominator and number of interior lattice points. Our approach is to first describe maximal polygons and then compute all subpolygons, where we eliminate redundancy by a suitable normal form. Executing our classification, we obtained a dataset of several billions of polygons covering a wide variety of cases.