## 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.

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 available | 2022 |
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Publisher | Zenodo |