IMath Webinar Series: Dom Vito Briones

You are all invited to attend the second webinar of the IMath Webinar Series for this semester on Monday, March 7, 2022, 2:00pm.

In this webinar (and graduate colloquium), Mr. Dom Vito A. Briones will present his work titled “Association Schemes on Triples”. Mr. Briones is a Ph.D. student in the institute working under the supervision of Prof. Jose Maria P. Balmaceda.

Abstract: In 1990, Mesner and Bhattaharya extended the notion of a classical association scheme to an association scheme on triples (AST), whose relations and adjacency algebra are ternary instead of binary. They showed that if a two-transitive group acts on a set \(\Omega\), then its orbits on \(\Omega \times \Omega \times \Omega\) is an AST. In this colloquium, we review how the sizes, third valencies, and intersection numbers of such ASTs are related to the actions of their two-transitive groups. We then determine these parameters for the ASTs obtained from the two-transitive groups \(A\Gamma L(k,n)\) for \(k\geq1\) and \(n\) a prime power.