Association schemes generated by a non-symmetric relation of valency 2

Hirasaka, Mitsugu; Muzychuk, Mikhail

doi:10.1016/s0012-365x(01)00063-2

Cited by 24 publications

(14 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paper continues the investigation of quasi-thin association schemes which were introduced in [6]. At the beginning of our study we thought that each quasi-thin association scheme was Schurian, i.e., a quotient of a thin scheme.…”

Section: Introductionmentioning

confidence: 57%

“…The number of the choices of (s, t) − 2), and, by Lemma 4.6, n C s, t [ n O h (F) . Therefore, the conclusion follows from (6)…”

Section: On Quasi-thin Association Schemes If W ] Z Then R(w Z) Is mentioning

confidence: 89%

“…Without loss of generality we may assume that (1, 1, 3), (1,2,4), (2,2,8), (2,6,12), (3,2,12), (3,5,15), (4,2,16), (4,14,28).…”

Section: Case 1 (|D|=0) This Condition Implies Thatmentioning

confidence: 99%

“…Moreover there was some evidence which confirmed this feeling. For example, it was shown that each quasi-thin scheme has a transitive automorphism group if and only if it is Schurian [6] and that each quasi-thin scheme of a square-free odd order is Schurian [5]. Nevertheless, it turned out that there are quasi-thin schemes which are not Schurian.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Quasi-thin Association Schemes

Hirasaka

Muzychuk

2002

Journal of Combinatorial Theory, Series A

View full text Add to dashboard Cite

An association scheme (or simply, a scheme) is called thin if each of its basic relations has valency 1. It is easy to see that thin schemes can be viewed as groups and, conversely, groups can be seen as thin schemes. In the present paper, we investigate schemes the basic relations of which have valency 1 or 2. We call these schemes quasi-thin. In order to formulate our results we let (X, R) denote a scheme (in the sense of P.-H. Zieschang). We first offer three sufficient conditions for (X, R) to have an automorphism group acting transitively on X. These conditions =4, |X|/4 ¥ {3, 4, 7, 8, 12, 16}. As a consequence of the latter result, we obtain a classification of the quasi-thin schemes with |X|=4p, where p is a prime number. © 2002 Elsevier Science (USA)

show abstract

Section: Introductionmentioning

confidence: 57%

“…The number of the choices of (s, t) − 2), and, by Lemma 4.6, n C s, t [ n O h (F) . Therefore, the conclusion follows from (6)…”

Section: On Quasi-thin Association Schemes If W ] Z Then R(w Z) Is mentioning

confidence: 89%