Haar graphical representations of finite groups and an application to poset representations
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Date
2025
Authors
Morris, Joy
Spiga, Pablo
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
Answering a question of Feng, Kovács, Wang, and Yang, we classify the finite groups admitting a Haar graphical representation. Specifically, we show that every finite group admits a Haar graphical representation, with abelian groups and ten other small groups as the only exceptions.
Our work on Haar graphs allows us to improve a 1980 result of Babai concerning representations of groups on posets, achieving the best possible result in this direction. An improvement to Babai's related result on representations of groups on distributive lattices follows.
Description
Open access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies
Keywords
Regular representation , Bipartite graph , Haar graph , Automorphism group , Graphical regular representation , DRR , GRR , Poset representation , Distributive lattice representation
Citation
Morris, J., & Spiga, P. (2025). Haar graphical representations of finite groups and an application to poset representations. Journal of Combinatorial Theory, Series B., 173, 279-304. https://doi.org/10.1016/j.jctb.2025.04.001