New Roses: Simple Symmetric Venn Diagrams with 11 and 13 Curves |
| |
Authors: | Khalegh Mamakani Frank Ruskey |
| |
Affiliation: | 1. Department of Computer Science, University of Victoria, Victoria, BC, Canada
|
| |
Abstract: | A symmetric (n) -Venn diagram is one that is invariant under (n) -fold rotation, up to a relabeling of curves. A simple (n) -Venn diagram is an (n) -Venn diagram 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 diagrams with crosscut symmetry, we found many simple symmetric Venn diagrams with 11 curves. The question of the existence of a simple 11-Venn diagram has been open since the 1960s. The technique used to find the 11-Venn diagram is extended and a symmetric 13-Venn diagram is also demonstrated. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|