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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.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20180611-L-Bamberg.html
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