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http://dx.doi.org/10.4134/BKMS.2015.52.5.1683

ON 4-EQUIVALENCED ASSOCIATION SCHEMES

PARK, JEONG RYE (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.52, no.5, 2015 , pp. 1683-1709 More about this Journal

Abstract

Let ( ${\Omega}$ , S) be an association scheme where ${\Omega}$ is a non-empty finite set and S is a partition of ${\Omega}{\times}{\Omega}$ . For a positive integer k we say that ( ${\Omega}$ , S) is k-equivalenced if each non-diagonal element of S has valency k. In this paper we focus on 4-equivalenced association schemes, and prove that they are transitive.

Keywords

association schemes; equivalenced; Frobenius; schurian; transitive;

Citations & Related Records

Reference

1	Z. Arad, Y. Erez, and M. Muzychuk, On even generalized table algebras, J. Algebraic Combin. 17 (2003), no. 2, 163-170. DOI
2	Z. Arad, Y. Erez, and M. Muzychuk, On homogeneous standard integral table algebras of degree 4, Comm. Algebra 34 (2006), no. 2, 463-519. DOI ScienceOn
3	E. Bannai and T. Ito, Algebraic Combinatorics. I, The Benjamin/Cummings Publishing Co., Inc., Menlo Park, CA, 1984.
4	C. J. Colbourn and J. H. Dinitz, Handbook of Combinatorial Designs, CRC press, 2010.
5	E. R. van Dam, A characterization of association schemes from affine spaces, Des. Codes Cryptogr. 21 (2000), no. 1-3, 83-86. DOI
6	J. D. Dixon and B. Mortimer, Permutation Groups, Graduate Texts in Mathematics, Vol. 163, Springer-Verlag, New York, 1996.
7	A. Hanaki and I. Miyamoto, Classification of association schemes with small vertices, published on web: http://math.shinshu-u.ac.jp/-hanaki/as/.
8	M. Hirasaka, K.-T. Kim, and J. R. Park, Every 3-equivalenced association scheme is Frobenius, J. Algebraic Combin. 41 (2015), no. 1, 217-228. DOI ScienceOn
9	M. Muzychuk and I. Ponomarenko, On pseudocyclic association schemes, Ars Math. Contemp. 5 (2012), no. 1, 1-25.
10	M. Muzychuk and P.-H. Zieschang, On association schemes all elements of which have valency 1 or 2, Discrete Math. 308 (2008), no. 14, 3097-3103. DOI ScienceOn
11	P.-H. Zieschang, An algebraic approach to association schemes, Lecture Notes in Math-ematics, Vol. 1628, Springer-Verlag, Berlin, 1996.
12	P.-H. Zieschang, Theory of Association Schemes, Springer Monograph in Mathematics, Springer-Verlag, Berlin, 2005.