Haar graphical representations of finite groups and an application to poset representations

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dc.contributor.authorMorris, Joy
dc.contributor.authorSpiga, Pablo
dc.date.accessioned2025-11-06T19:06:57Z
dc.date.available2025-11-06T19:06:57Z
dc.date.issued2025
dc.descriptionOpen access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies
dc.description.abstractAnswering 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.
dc.description.peer-reviewYes
dc.identifier.citationMorris, 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
dc.identifier.urihttps://hdl.handle.net/10133/7222
dc.language.isoen
dc.publisherElsevier
dc.publisher.departmentDepartment of Mathematics and Computer Science
dc.publisher.facultyArts and Science
dc.publisher.institutionUniversity of Lethbridge
dc.publisher.institutionUniversity of Milano-Biococca
dc.publisher.urlhttps://doi.org/10.1016/j.jctb.2025.04.001
dc.subjectRegular representation
dc.subjectBipartite graph
dc.subjectHaar graph
dc.subjectAutomorphism group
dc.subjectGraphical regular representation
dc.subjectDRR
dc.subjectGRR
dc.subjectPoset representation
dc.subjectDistributive lattice representation
dc.titleHaar graphical representations of finite groups and an application to poset representations
dc.typeArticle
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