Primitive commutative association schemes with a non-symmetric relation ofvalency 3

Authors
Hirasaka, M
Citation
M. Hirasaka, Primitive commutative association schemes with a non-symmetric relation ofvalency 3, J COMB TH A, 90(1), 2000, pp. 27-48
Citations number
8
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF COMBINATORIAL THEORY SERIES A
ISSN journal
00973165 → ACNP
Volume
90
Issue
1
Year of publication
2000
Pages
27 - 48
Database
ISI
SICI code
0097-3165(200004)90:1<27:PCASWA>2.0.ZU;2-9
Abstract
Let (X, {R-i} (0) (less than or equal to) (i) (less than or equal to) (d)) be a primitive commutative association scheme. If there is a non-symmetric relation R-i with valency 3, then the cardinality of X is equal to either p or p(2) where p is an odd prime. Moreover, if \X\ = p then (X, {R-i} (0) ( less than or equal to) (i) (less than or equal to d)) is isomorphic to a cy clotomic scheme. (C) 2000 Academic Press.