March 29, 2024
Reza Sharafdini

Reza Sharafdini

Academic Rank: Associate professor
Address:
Degree: Ph.D in Mathematics - Algebra
Phone: 77-31222750
Faculty: Faculty of Intelligent Systems and Data Science

Research

Title Coherent configurations over copies of association schemes of prime order
Type Article
Keywords
Journal ARS Mathematica Contemporanea
DOI
Researchers Reza Sharafdini (First researcher) ,

Abstract

Let $G$ be a group acting faithfully and transitively on $\Omega_i$ for $i=1,2$. A famous theorem by Burnside implies the following fact: If $|\Omega_1|=|\Omega_2|$ is a prime and the rank of one of the actions is greater than two, then the actions are equivalent, or equivalently $|(\alpha,\beta)^G|=|\Omega_1|=|\Omega_2|$ for some $(\alpha,\beta)\in \Omega_1\times \Omega_2$. In this paper we consider a combinatorial analogue to this fact through the theory of coherent configurations, and give some arithmetic sufficient conditions for a coherent configuration with two homogeneous components of prime order to be uniquely determined by one of the homogeneous components.