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

• Published in 2012
• Added on 2012-08-09

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.

Links

• http://arxiv.org/abs/1207.6452
• http://arxiv.org/pdf/1207.6452v1

Other information

BibTeX entry

@article{Mamakani2012,
	key = {Mamakani2012},
	type = {article},
	title = {A New Rose : The First Simple Symmetric 11-Venn Diagram},
	author = {Mamakani, Khalegh and Ruskey, Frank},
	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.},
	comment = {},
	date_added = {2012-08-09},
	date_published = {2012-07-01},
	urls = {http://arxiv.org/abs/1207.6452,http://arxiv.org/pdf/1207.6452v1},
	collections = {Art,Easily explained},
	archivePrefix = {arXiv},
	arxivId = {1207.6452},
	eprint = {1207.6452},
	keywords = {crosscut symmetry,hypercube,symmetric graphs,venn diagram},
	month = {jul},
	url = {http://arxiv.org/abs/1207.6452 http://arxiv.org/pdf/1207.6452v1},
	year = 2012,
	primaryClass = {cs.CG},
	urldate = {2012-08-09}
}