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DOI: 10.4230/LIPIcs.SOCG.2015.19

Automatic Proofs for Formulae Enumerating Proper Polycubes

Authors: Gill Barequet and Mira Shalah

Published in: LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)

Abstract

This video describes a general framework for computing formulae enumerating polycubes of size n which are proper in n-k dimensions (i.e., spanning all n-k dimensions), for a fixed value of k. (Such formulae are central in the literature of statistical physics in the study of percolation processes and collapse of branched polymers.) The implemented software re-affirmed the already-proven formulae for k <= 3, and proved rigorously, for the first time, the formula enumerating polycubes of size n that are proper in n-4 dimensions.

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Gill Barequet and Mira Shalah. Automatic Proofs for Formulae Enumerating Proper Polycubes. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 19-22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{barequet_et_al:LIPIcs.SOCG.2015.19,
  author =	{Barequet, Gill and Shalah, Mira},
  title =	{{Automatic Proofs for Formulae Enumerating Proper Polycubes}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{19--22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Arge, Lars and Pach, J\'{a}nos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.19},
  URN =		{urn:nbn:de:0030-drops-50889},
  doi =		{10.4230/LIPIcs.SOCG.2015.19},
  annote =	{Keywords: Polycubes, inclusion-exclusion}
}

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Automatic Proofs for Formulae Enumerating Proper Polycubes

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