# Lecture by John Bamberg (University of Western Australia, Perth): Bruck nets, metric planes, and their friends

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 incidence structures that do not involve the ‘three-reflection theorem’ whatsoever, and thus yields a beautiful characterisation of the finite affine planes 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 Sherk planes*. In this talk, we outline our characterisation of these incidence structures as *Bruck nets*, in the same vein as Sherk’s result, and what it means for connected combinatorial objects such as mutually orthogonal latin squares.

(Joint work with Joanna Fawcett and Jesse Lansdown)

### Time & Location

Jun 11, 2018 | 02:15 PM

Freie Universität Berlin

Institut für Informatik

Takustr. 9

14195 Berlin

room 005 (ground floor)

Campus map