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Pach’s Animal Problem Within the Bounding Box

Author Martin Tancer

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LIPIcs.SoCG.2024.78.pdf
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Martin Tancer
  • Department of Applied Mathematics, Charles University, Prague, Czech Republic

Funding

Supported by the GAČR grant no. 22-19073S.

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Martin Tancer. Pach’s Animal Problem Within the Bounding Box. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 78:1-78:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SoCG.2024.78

Abstract

A collection of unit cubes with integer coordinates in ℝ³ is an animal if its union is homeomorphic to the 3-ball. Pach’s animal problem asks whether any animal can be transformed to a single cube by adding or removing cubes one by one in such a way that any intermediate step is an animal as well. Here we provide an example of an animal that cannot be transformed to a single cube this way within its bounding box.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Animal problem
  • bounding box
  • non-shellable balls

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