q-Analogs of Steiner Systems with t>1 do Exist
Speaker: Professor Alfred Wassermann (Univ. Bayreuth)
Time: 4.00 PM
Date: Monday 22nd April 2013
Location: Casl Seminar Room (Belfield Office Park)
Abstract:
A q-analog of a Steiner system, denoted by S_q(t,k,n), is a set of k-dimensional subspaces of F_q^n such that each t-dimensional subspace of F_q^n is contained in exactly one element of S_q(t,k,n). In the talk the construction of the first known nontrivial q-Steiner system with t>1 will be described. Specifically, S_2(2,3,13) q-Steiner} systems have been found by requiring that their automorphism group contain the normalizer of a Singer subgroup of GL(13,2). This approach leads to an instance of the exact cover problem, which turns out to have many solutions. There is no reason to believe that this would be the only set of parameters for which q-Steiner systems exist.
This is joint work with M. Braun, T. Etzion, P. Ostergard and A. Vardy.
Series: Algebra Seminar Series
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