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DESCRIPTION: A pseudocircle is a simple closed curve in the plane. An inter
 secting arrangement of pseudocircles is a finite collection of pseudocircle
 s so that any two intersect in exactly two points where they cross. Grünbau
 m conjectured in the 1970's that in the case of simple arrangements there a
 re at most 2n - 2 digon cells\, i.e. cells which have exactly two crossings
  on its boundary. I will present a result by Agarwal et al. (2004) which pr
 oves this conjecture for the special case of cylindrical arrangements. Base
 d on that we show that the conjecture also holds whenever the arrangement c
 ontains three pseudocircles which pairwise form a digon cell. Moreover\, I 
 will present a result concerning the number of triangles in digon free arra
 ngements\, which disproves another conjecture by Grünbaum. (joint with S.Fe
 lsner and M.Scheucher) 
DTSTAMP:20220511T193800
DTSTART:20220516T160000
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
 es 17. Juni 136\n 10623 Berlin\n Room MA 041 (Ground Floor)\n 
SEQUENCE:0
SUMMARY:Sandro Roch (Technische Universität Berlin): Arrangements of Pseudo
 circles: On Digons and Triangles
UID:107920318@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20220516-C-Roch.html
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