Computing all the simple symmetric monotone venn diagrams on seven curves
Date
2001
Authors
Cao, Tao
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Abstract
A family of intersecting simple closed curves (FISC) 1s a collection of simple closed curves in the plane with the properties that there is some open region common to the interiors of all the curves, and that every two curves intersect in finitely many points. A normal FISC, or NFISC is a FISC with the properĀ ties that each curve touches the outer face and the family is convex-drawable. In this thesis, we present a G-encoding technique for an NFISC, which generĀalizes a Grunbaum encoding for a simple monotone Venn diagram. We prove that NFISC diagrams can be uniquely identified with their G-encodings, and simple monotone Venn diagrams can be identified with their Grunbaum encodings. By applying this theory, we develop two algorithms to search all possible simple symmetric monotone (SSM) Venn diagrams with seven curves.The total number of such diagrams is 23.