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no. 3
Weights on homogeneous coherent configurations
Hanaki, Akihide1
1 Faculty of Science Shinshu University Matsumoto 390-8621 Japan
Algebraic Combinatorics, Volume 8 (2025) no. 3, pp. 765-773.

D. G. Higman generalized the notion of a coherent configuration and defined a weight. In this article, we will modify the definition and investigate weights on coherent configurations. If our weights are on a thin homogeneous coherent configuration, that is essentially a finite group, then there is a natural correspondence between the set of equivalence classes of weights and the $2$-cohomology group of the group. We also give a construction of weights as a generalization of Higman’s method using monomial representations of finite groups.

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Accepted:
Published online:
DOI: 10.5802/alco.420
Classification: 05E30
Keywords: homogeneous coherent configuration, weight, association scheme, factor set, cohomology

Hanaki, Akihide 1

1 Faculty of Science Shinshu University Matsumoto 390-8621 Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Hanaki, Akihide. Weights on homogeneous coherent configurations. Algebraic Combinatorics, Volume 8 (2025) no. 3, pp. 765-773. doi : 10.5802/alco.420. https://alco.centre-mersenne.org/articles/10.5802/alco.420/

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