Torsten Mütze

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math.CO2025

On minimum Venn diagrams

Sofia Brenner, Petr Gregor, Torsten Mütze +1

An $n$ -Venn diagram is a diagram in the plane consisting of $n$ simple closed curves that intersect only finitely many times such that each of the $2^{n}$ possible intersections is r…

math.CO2025

Combinatorial generation via permutation languages. VII. Supersolvable hyperplane arrangements

Sofia Brenner, Jean Cardinal, Thomas McConville +2

For an arrangement $H$ of hyperplanes in $R^{n}$ through the origin, a region is a connected subset of $R^{n} ∖ H$ . The graph of regions $G(…

math.CO2025

Disproving two conjectures on the Hamiltonicity of Venn diagrams

Sofia Brenner, Linda Kleist, Torsten Mütze +2

In 1984, Winkler conjectured that every simple Venn diagram with $n$ curves can be extended to a simple Venn diagram with $n + 1$ curves. His conjecture is equivalent to the statemen…