Abstract:
Configurations are finite incidence structures where each point is on $t+1$ lines, each line has $s+1$ points and any two distinct points are incident with at most one line. They are sometimes also called partial linear spaces of order $(s,t)$. My talk will be on how to give the set of existing configurations the structure of a numerical semigroup and about what happens when we restrict to configurations without triangles, quadrangles and generally, $n$-gons. If I have time I will also talk about configurations used in a protocol for User-Private Information Retrieval (uPIR).