ALGEBRAIC COMBINATORICS

no. 1
Combinatorial Hopf algebras from representations of families of wreath products
Crisp, Tyrone1; Hill, Caleb Kennedy1
1 Department of Mathematics & Statistics University of Maine 5752 Neville Hall, Room 333 Orono ME 04469 USA
Algebraic Combinatorics, Volume 5 (2022) no. 1, pp. 93-120.

We construct Hopf algebras whose elements are representations of combinatorial automorphism groups, by generalising a theorem of Zelevinsky on Hopf algebras of representations of wreath products. As an application we attach symmetric functions to representations of graph automorphism groups, generalising and refining Stanley’s chromatic symmetric function.

Received:
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Accepted:
Published online:
DOI: 10.5802/alco.198
Classification: 05E10, 16T30, 20C15
Keywords: Combinatorial Hopf algebra, PSH algebra, wreath product, chromatic symmetric function
Crisp, Tyrone 1; Hill, Caleb Kennedy 1

1 Department of Mathematics & Statistics University of Maine 5752 Neville Hall, Room 333 Orono ME 04469 USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Crisp, Tyrone; Hill, Caleb Kennedy. Combinatorial Hopf algebras from representations of families of wreath products. Algebraic Combinatorics, Volume 5 (2022) no. 1, pp. 93-120. doi : 10.5802/alco.198. https://alco.centre-mersenne.org/articles/10.5802/alco.198/

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