On pseudocyclic association schemes

Mikhail Muzychuk; Ilya Ponomarenko

doi:10.26493/1855-3974.121.885

On pseudocyclic association schemes

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Abstract

The notion of a pseudocyclic association scheme is generalized to the non-commutativecase. It is proved that any pseudocyclic scheme the rank of which is much more than the valency is the scheme of a Frobenius group and is uniquely determined up to isomorphism by its intersection number array. An immediate corollary of this result is that any scheme of prime degree, valency k and rank at least k⁴ is schurian.

Original language	American English
Pages (from-to)	1-25
Number of pages	25
Journal	Ars Mathematica Contemporanea
Volume	5
Issue number	1
DOIs	https://doi.org/10.26493/1855-3974.121.885
State	Published - 1 Jan 2012
Externally published	Yes

Keywords

Association schemes
Frobenius groups
Pseudocyclic schemes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Algebra and Number Theory
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.26493/1855-3974.121.885

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AB - The notion of a pseudocyclic association scheme is generalized to the non-commutativecase. It is proved that any pseudocyclic scheme the rank of which is much more than the valency is the scheme of a Frobenius group and is uniquely determined up to isomorphism by its intersection number array. An immediate corollary of this result is that any scheme of prime degree, valency k and rank at least k4 is schurian.

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On pseudocyclic association schemes

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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