Database of small Schurian association schemes

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.

本数据库收录了阶数为2至48的（未必交换的）舒尔结合方案（Schurian association schemes）。该数据库的详细信息已发表于论文《小型舒尔结合方案普查》（A census of small Schurian association schemes）。阶数为N的舒尔结合方案存储于文件“SchurianSchemesN”中。该文件的每一行均包含列表[关联矩阵（Relmat）、生成元（Generators）、传递识别标识（TransitiveIdentification）、特征标表（CharacterTable）、重数（Multiplicities）]，各字段含义如下：
- 关联矩阵（Relmat）：用于描述结合方案的关系矩阵
- 生成元（Generators）：可生成该结合方案全自同构群的置换群
- 传递识别标识（TransitiveIdentification）：该自同构群在GAP与MAGMA的传递群库中的识别标识
- 特征标表（CharacterTable）：对应结合方案的特征标表
- 重数（Multiplicities）：列表的第i项对应特征标表第i行中特征标的重数
需注意，部分特征标表条目使用GAP记号E(n)来表示本原n次单位根，此类内容可直接在GAP中读取，但若需在其他软件包中使用则可能需要进行格式转换。