Signatures of graphs for bicommutative Hopf algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909552469868544 |
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| author | Caudillo, Diego Diehl, Joscha Ebrahimi-Fard, Kurusch Verri, Emanuele |
| author_facet | Caudillo, Diego Diehl, Joscha Ebrahimi-Fard, Kurusch Verri, Emanuele |
| contents | This article approaches the counting of subgraphs, in terms of signature-type functionals defined over combinatorial Hopf algebras of graphs. Well-known algebraic identities that arise in the context of counting subgraphs are then captured by their character property and a type of "Chen's identity". While different notions of subgraphs (and homomorphisms) correspond to different combinatorial Hopf algebras on graphs, we will show that they are all isomorphic to a polynomial Hopf algebra. In addition, the isomorphy between the Hopf algebras can be realized by maps that respect the counting operations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_08323 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Signatures of graphs for bicommutative Hopf algebras Caudillo, Diego Diehl, Joscha Ebrahimi-Fard, Kurusch Verri, Emanuele Rings and Algebras Combinatorics This article approaches the counting of subgraphs, in terms of signature-type functionals defined over combinatorial Hopf algebras of graphs. Well-known algebraic identities that arise in the context of counting subgraphs are then captured by their character property and a type of "Chen's identity". While different notions of subgraphs (and homomorphisms) correspond to different combinatorial Hopf algebras on graphs, we will show that they are all isomorphic to a polynomial Hopf algebra. In addition, the isomorphy between the Hopf algebras can be realized by maps that respect the counting operations. |
| title | Signatures of graphs for bicommutative Hopf algebras |
| topic | Rings and Algebras Combinatorics |
| url | https://arxiv.org/abs/2206.08323 |