License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SOCG.2015.19
URN: urn:nbn:de:0030-drops-50889
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5088/
Go to the corresponding LIPIcs Volume Portal

Barequet, Gill ; Shalah, Mira

Automatic Proofs for Formulae Enumerating Proper Polycubes

pdf-format:
5.pdf (0.4 MB)

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.

BibTeX - Entry

@InProceedings{barequet_et_al:LIPIcs:2015:5088,
  author =	{Gill Barequet and Mira Shalah},
  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 =	{Lars Arge and J{\'a}nos Pach},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5088},
  URN =		{urn:nbn:de:0030-drops-50889},
  doi =		{10.4230/LIPIcs.SOCG.2015.19},
  annote =	{Keywords: Polycubes, inclusion-exclusion}
}

Keywords: Polycubes, inclusion-exclusion
Collection: 31st International Symposium on Computational Geometry (SoCG 2015)
Issue Date: 2015
Date of publication: 12.06.2015

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI