Association schemes and Hypergroups
Combinatorics
2017-04-24 v2 Group Theory
Abstract
In this paper, we investigate hypergroups which arise from association schemes in a canonical way; this class of hypergroups is called realizable. We first study basic algebraic properties of realizable hypergroups. Then we prove that two interesting classes of hypergroups (partition hypergroups and linearly ordered hypergroups) are realizable. Along the way, we prove that a certain class of projective geometries is equipped with a canonical association scheme structure which allows us to link three objects; association schemes, hypergroups, and projective geometries.
Cite
@article{arxiv.1607.05086,
title = {Association schemes and Hypergroups},
author = {Jaiung Jun},
journal= {arXiv preprint arXiv:1607.05086},
year = {2017}
}
Comments
Section 6 is removed and the preprint is reduced to its essentials. Also, several minor mistakes are corrected