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• digon-free arrangements of up to $n=14$ pseudocircles which obtain the minimum number of triangles,
• 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
• 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

File: triangles/digonfree_minimal_triangles/all3_df_8_triangles.txt (193 bytes)

File: triangles/digonfree_minimal_triangles/all4_df_8_triangles.txt (822 bytes)

File: triangles/digonfree_minimal_triangles/all5_df_8_triangles.txt (717 bytes)

File: triangles/digonfree_minimal_triangles/some13_df_18_triangles.txt (149.31 KB)

### Digonfree arrangement maximizing the number of triangles

File: triangles/digonfree_maximal_triangles/all5_df_12_triangles.enc (271 bytes)

File: triangles/digonfree_maximal_triangles/all6_df_20_triangles.enc (258 bytes)

File: triangles/digonfree_maximal_triangles/all7_df_29_triangles.enc (317 bytes)

File: triangles/digonfree_maximal_triangles/some8_df_37_triangles.enc (985 bytes)

File: triangles/digonfree_maximal_triangles/some9_df_48_triangles.enc (200 bytes)

#### Fueredi Palasti Construction

This family of circularizable arrangements with $\lim_{n \to \infty} p_3/n^2 = 2/3$.

File: triangles/fueredi_palasti_construction/fueredi_palasti_6.enc (66 bytes)

File: triangles/fueredi_palasti_construction/fueredi_palasti_12.enc (423 bytes)

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Last update: January 16 2021 10:55:40. (c) 2017 Stefan Felsner and Manfred Scheucher