Separability Number and Schurity Number of Coherent Configurations

To each coherent configuration (scheme) C and positive integer m we associate a natural scheme C(m) on the m-fold Cartesian product of the point set of C having the same automorphism group as C. Using this construction we define and study two positive integers: the separability number s(C) and the Schurity number t(C) of C. It turns out that s(C) m iff C is uniquely determined up to isomorphism by the intersection numbers of the scheme C(m). Similarly, t(C) m iff the diagonal subscheme of C(m) is an orbital one. In particular, if C is the scheme of a distance-regular graph , then s(C) = 1 iff is uniquely determined by its parameters whereas t(C) = 1 iff is distance-transitive. We show that if C is a Johnson, Hamming or Grassmann scheme,

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Sergei Evdokimov, Ilia N. Ponomarenko
• Keywords: Coherent Configuration, COMBINATORICS 2000, M-fold Cartesian Product, Positive Integers