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COMBINATORICS
2000

Separability Number and Schurity Number of Coherent Configurations

13 years 11 months ago
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,
Sergei Evdokimov, Ilia N. Ponomarenko
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2000
Where COMBINATORICS
Authors Sergei Evdokimov, Ilia N. Ponomarenko
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