Interesting Esoterica

A New Rose : The First Simple Symmetric 11-Venn Diagram

Article by Mamakani, Khalegh and Ruskey, Frank
  • Published in 2012
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A symmetric Venn diagram is one that is invariant under rotation, up to a relabeling of curves. A simple Venn diagram is one in which at most two curves intersect at any point. In this paper we introduce a new property of Venn diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer search restricted to crosscut symmetry we found many simple symmetric Venn diagrams with 11 curves. This answers an existence question that has been open since the 1960's. The first such diagram that was discovered is shown here.

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arxivId
1207.6452
keywords
crosscut symmetry,hypercube,symmetric graphs,venn diagram

BibTeX entry

@article{Mamakani2012,
	abstract = {A symmetric Venn diagram is one that is invariant under rotation, up to a relabeling of curves. A simple Venn diagram is one in which at most two curves intersect at any point. In this paper we introduce a new property of Venn diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer search restricted to crosscut symmetry we found many simple symmetric Venn diagrams with 11 curves. This answers an existence question that has been open since the 1960's. The first such diagram that was discovered is shown here.},
	archivePrefix = {arXiv},
	arxivId = {1207.6452},
	author = {Mamakani, Khalegh and Ruskey, Frank},
	eprint = {1207.6452},
	keywords = {crosscut symmetry,hypercube,symmetric graphs,venn diagram},
	month = {jul},
	title = {A New Rose : The First Simple Symmetric 11-Venn Diagram},
	url = {http://arxiv.org/abs/1207.6452 http://arxiv.org/pdf/1207.6452v1},
	year = 2012,
	primaryClass = {cs.CG},
	urldate = {2012-08-09},
	collections = {Art,Easily explained}
}