Q-analogues of Steiner systems with $t\geq 2$ do exist
Speaker: Alfred Wassermann (University of Bayreuth, Germany)
Time: 4.00 PM
Date: Monday February 25th 2013
Location: Casl Seminar Room (Belfield Office Park)
Abstract:
A $q$-analog of a Steiner system, denoted by $\dS = \dS_q[t,k,n]$, 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 $\dS$. In the talk the construction of the first known nontrivial $q$-Steiner system with $t \geq 2$ will be described. Specifically, $\dS_2[2,3,13]$ \mbox{$q$-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. \"Osterg{\aa}rd and A. Vardy.
Series: Algebra Seminar Series
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