A census of small Schurian association schemes

Jesse Lansdown

doi:10.1142/S0218196723500674

A census of small Schurian association schemes

Jesse Lansdown

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

Abstract

Using the classification of transitive groups of degree n, for 2≤n≤48, we classify the Schurian association schemes of order n, and as a consequence, the transitive groups of degree n that are 2-closed. In addition, we compute the character table of each association scheme and provide a census of important properties. Finally, we compute the 2-closure of each transitive group of degree n, for 2≤n≤48. The results of this classification are made available as a supplementary database.

Original language	English
Pages (from-to)	23-33
Number of pages	11
Journal	International Journal of Algebra and Computation
Volume	34
Issue number	1
DOIs	https://doi.org/10.1142/S0218196723500674
Publication status	Published - 1 Feb 2024
Externally published	Yes

Keywords

2-closed permutation groups
Homogeneous coherent configuration, association scheme
Schurian

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10.1142/S0218196723500674

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abstract = "Using the classification of transitive groups of degree n, for 2≤n≤48, we classify the Schurian association schemes of order n, and as a consequence, the transitive groups of degree n that are 2-closed. In addition, we compute the character table of each association scheme and provide a census of important properties. Finally, we compute the 2-closure of each transitive group of degree n, for 2≤n≤48. The results of this classification are made available as a supplementary database.",

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AB - Using the classification of transitive groups of degree n, for 2≤n≤48, we classify the Schurian association schemes of order n, and as a consequence, the transitive groups of degree n that are 2-closed. In addition, we compute the character table of each association scheme and provide a census of important properties. Finally, we compute the 2-closure of each transitive group of degree n, for 2≤n≤48. The results of this classification are made available as a supplementary database.

KW - 2-closed permutation groups

KW - Homogeneous coherent configuration, association scheme

KW - Schurian

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DO - 10.1142/S0218196723500674

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JO - International Journal of Algebra and Computation

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A census of small Schurian association schemes

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Keywords

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