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Jaiung Jun (전재웅), On the Hopf algebra of multi-complexes

Thursday, December 17, 2020 @ 10:00 AM - 11:00 AM KST

Zoom ID: 869 4632 6610 (ibsdimag)


Jaiung Jun (전재웅)
Department of Mathematics, SUNY New Paltz

In combinatorics, Hopf algebras appear naturally when studying various classes of combinatorial objects, such as graphs, matroids, posets or symmetric functions. Given such a class of combinatorial objects, basic information on these objects regarding assembly and disassembly operations are encoded in the algebraic structure of a Hopf algebra. One then hopes to use algebraic identities of a Hopf algebra to return to combinatorial identities of combinatorial objects of interest.

In this talk, I introduce a general class of combinatorial objects, which we call multi-complexes, which simultaneously generalizes graphs, hypergraphs and simplicial and delta complexes. I also introduce a combinatorial Hopf algebra obtained from multi-complexes. Then, I describe the structure of the Hopf algebra of multi-complexes by finding an explicit basis of the space of primitives, which is of combinatorial relevance. If time permits, I will illustrate some potential applications.

This is joint work with Miodrag Iovanov.


Thursday, December 17, 2020
10:00 AM - 11:00 AM KST
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Zoom ID: 869 4632 6610 (ibsdimag)


Jaehoon Kim (김재훈)
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IBS 이산수학그룹 Discrete Mathematics Group
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