Database of small Schurian association schemes

Dataset

Description

This database contains the (not necessarily commutative) Schurian association schemes of order 2 to 48. The details of this database are reported in the paper "A census of small Schurian association schemes".

The Schurian association schemes of order N are contained in the file "SchurianSchemesN". Each line of the file contains the list
    [ Relmat, Generators, TransitiveIdentification, CharacterTable, Multiplicities]
where:
- Relmat is the relation matrix describing an association scheme
- Generators are permutations which generate the full automorphism group of the association scheme
- TransitiveIdentification is the identification for the automorphism group in the transitive groups libraries of GAP and MAGMA
- CharacterTable is the character table of the association scheme
- The i-th entry of Multiplicities is the multiplicity of the character in the i-th row of the character table

Note that some entries of the character tables use the GAP notation E(n) to describe a primitive n-th root of unity, meaning that they can be read directly by GAP but conversion may be required for use in other software packages.
Date made available2022
PublisherZenodo

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