Symmetric Monotone Venn Diagrams with Seven Curves
Tao Cao,
Department of Computer Science,
University of Victoria, Canada.
Khalegh Mamakani,
Department of Computer Science,
University of Victoria, Canada.
Frank Ruskey,
Department of Computer Science,
University of Victoria, Canada.
Abstract:
An nVenn diagram consists of n curves drawn in the plane in
such a way that each of the 2^{n} possible intersections of the
interiors and exteriors of the curves forms a connected nonempty region.
A kregion in a diagram is a region that is in the interior of precisely
k curves.
A nVenn diagram is symmetric if it has a point of
rotation about which
rotations of the plane by 2\pi/n radians leaves the diagram fixed;
it is polar symmetric if it is symmetric and its stereographic
projection about the infinite outer face is isomorphic to the
projection about the innermost face.
A Venn diagram is monotone if every kregion is adjacent
to both some (k1)region (if k > 0) and also to some
k+1 region (if k < n).
A Venn diagram is simple if at most two curves intersect at any point.
We prove that the socalled Grunbaum encoding uniquely identifies monotone
symmetric nVenn diagrams
and describe an algorithm that produces an exhaustive list of
all of the monotone symmetric nVenn diagrams.
That algorithm is used to prove that there are exactly 23 simple monotone
symmetric 7Venn diagrams, of which 6 are polar symmetric.

An A0 sized poster (2.5 megabytes).

Files: pdf.

Fifth International Conference on Fun with Algorithms, Ischia Island, Italy.
Lecture Notes in Computer Science, LNCS, to appear.

Submitted January 22, 2010.

Please send me a note if
you download one of these files.
It's always nice to know who's reading your papers.

Here is Khalegh's talk from the FUN conference:
KhaleghVennFun.pdf
(5 megabytes).

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