报告题目:Testing isomorphism of cyclic symmetric configurations

报告学者:Istvan Kovacs教授

报告者单位Primorska University



摘要:A symmetric (combinatorial) configuration of type $(n_k)$ is an incidence geometry $(X,L)$, consisting of a set $X$ of $n$ points and a collection $L \subset 2^X$ of $n$ lines (or blocks) such that distinct lines intersect in at most one point, and all lines contain $k \ge 3$ points.  A cyclic configuration has point set $X=\mathbb{Z}_n$, such that the mapping $x \mapsto x+1$, preserves the lines. Two such configurations are said to be multiplier equivalent if one can be mapped to the other by a mapping in the form $x \mapsto mx$, where $m$ is relatively prime to $n$. It is easy to see that multiplier equivalent configurations are isomorphic. In this talk, I will show that the converse also holds, and hence give a simple isomorphism criterion for cyclic symmetric configurations. As an application, a

formula will also be shown for the number of symmetric cyclic configurations of type $(n_3)$. The talk is based on joint work with Hiroki Koike, Dragan Maru\v{s}i\v{c}, Mikhail Muzychuk and Toma\v{z} Pisanski