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This page provides
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digon-free arrangements of up to $n=14$ pseudocircles which obtain the minimum number of triangles,
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arrangements of up to $n=7$ pseudocircles which obtain the maximum number of triangles
(and some examples for $n=8,9$ which might be optimal), and
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small instances of an infinite family of arrangements which obtain an asymptotical triangle-cell-ratio of $2/3$.
For details, please see
Arrangements of Pseudocircles: Triangles and Drawings.
Digonfree arrangement minimizing the number of triangles
Digonfree arrangement maximizing the number of triangles
Fueredi Palasti Construction
This family of circularizable arrangements with $\lim_{n \to \infty} p_3/n^2 = 2/3$.
Go back...Last update: July 09 2022 12:31:27.
(c) 2017 Stefan Felsner and Manfred Scheucher