Discrete mathematics seminar - Representations of groups and inverse semigroups on (uniform) hypergraphs

Dates

Wednesday, January 4, 2023 - 14:00 to 15:00

Speaker: Tatiana Jajcayová (Comenius University, Bratislava)

Abstract: In our talk, we will discuss our project of constructing uniform hypergraphs whose full automorphism group is isomorphic to a prescribed finite group G and acts regularly on the vertices of the hypergraph. This project is a generalization of the classical problem of Graphical Regular Representations and relies on a generalization of Cayley graphs to Cayley hypergraphs. 

We will then turn our attention to the more general concept of partial automorphisms which we believe better captures local properties of the considered combinatorial structures. In the context of partial automorphisms, we address analogous questions of representing hypergraphs via inverse semigroups.