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DESCRIPTION: In 1967\, F. Arthur Sherk gave a simple proof that the finite 
 metric planes (of Bachmann and Schmidt) are precisely the affine planes of 
 odd order. Moreover\, Sherk’s proof holds for a more general class of incid
 ence structures that do not involve the ‘three-reflection theorem’ whatsoev
 er\, and thus yields a beautiful characterisation of the finite affine plan
 es of odd order. By relaxing the first of Sherk’s axioms to ‘every pair of 
 points lies on  at most  one line’\, we can study what we call  partial She
 rk planes . In this talk\, we outline our characterisation of these inciden
 ce structures as  Bruck nets \, in the same vein as Sherk’s result\, and wh
 at it means for connected combinatorial objects such as mutually orthogonal
  latin squares.   (Joint work with Joanna Fawcett and Jesse Lansdown) 
DTSTAMP:20180611T135500
DTSTART:20180611T141500
CLASS:PUBLIC
LOCATION:Freie Universität Berlin\n Institut für Informatik\n Takustr. 9\n 
 14195 Berlin\n room 005 (ground floor)
SEQUENCE:0
SUMMARY:John Bamberg (University of Western Australia\, Perth): Bruck nets\
 , metric planes\, and their friends
UID:89454950@/www.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20180611-L-Bam
 berg.html
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