On quasi-thin association schemes

Mikhail Muzychuk, Ilya Ponomarenko

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

An association scheme is called quasi-thin if each of its basic relations has valency 1 or 2. A quasi-thin scheme is called Kleinian if its thin residue is the Klein four-group with respect to relational multiplication. It is proved that any Kleinian quasi-thin scheme arises from a near-pencil on 3 points, from an affine plane of order 2, or from a projective plane of order 2. The main result in this paper is that any non-Kleinian quasi-thin scheme is schurian and separable. We also construct an infinite family of Kleinian quasi-thin schemes which is neither schurian nor separable.

Original languageEnglish
Pages (from-to)467-489
Number of pages23
JournalJournal of Algebra
Volume351
Issue number1
DOIs
StatePublished - 1 Feb 2012
Externally publishedYes

Keywords

  • Association schemes
  • Coherent configurations
  • Quasi-thin schemes
  • Schurian schemes

ASJC Scopus subject areas

  • Algebra and Number Theory

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