The NonKrupp subarrangement conjecture for pseudocircle arrangements
The NonKrupp subarrangement conjecture for pseudocircle arrangements
Let be a connected digon-free arrangement of pseudocircles. A triple of pseudocircles forms a triangle in when its three pseudocircles bound such a triangular cell, and it is NonKrupp when it is not a Krupp configuration. Let denote the specified arrangement of six pseudocircles.
NonKrupp subarrangement conjecture. If every triple of pseudocircles which forms a triangle in is NonKrupp, then contains as a subarrangement.
All arrangements known to be non-circularizable by the stated theorem contain as a subarrangement, motivating this conjecture. Its resolution is not given in the source.
Sources & referencesView supporting material
Primary source
Stefan Felsner and Manfred Scheucher, “Arrangements of Pseudocircles: On Circularizability”, arXiv:1712.02149 (2020).
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