On the Hopf superalgebra of symmetric functions in superspace
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915475960627200 |
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| author | Hattori, Masamune Yagi, Renta Yanagida, Shintarou |
| author_facet | Hattori, Masamune Yagi, Renta Yanagida, Shintarou |
| contents | We introduce a superspace analogue of combinatorial Hopf algebras (Aguiar-Bergeron-Sottile, 2006), and show that the Hopf superalgebra of quasi-symmetric (resp. symmetric) functions in superspace (Fishel-Lapointe-Pinto, 2019) is a terminal object in the category of all (resp. cocommutative) combinatorial Hopf superalgebras. We also introduce a superspace analogue of chromatic symmetric functions of graphs (Stanley, 1995) using the chromatic Hopf superalgebra of two-colored graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Hopf superalgebra of symmetric functions in superspace Hattori, Masamune Yagi, Renta Yanagida, Shintarou Combinatorics Mathematical Physics Quantum Algebra We introduce a superspace analogue of combinatorial Hopf algebras (Aguiar-Bergeron-Sottile, 2006), and show that the Hopf superalgebra of quasi-symmetric (resp. symmetric) functions in superspace (Fishel-Lapointe-Pinto, 2019) is a terminal object in the category of all (resp. cocommutative) combinatorial Hopf superalgebras. We also introduce a superspace analogue of chromatic symmetric functions of graphs (Stanley, 1995) using the chromatic Hopf superalgebra of two-colored graphs. |
| title | On the Hopf superalgebra of symmetric functions in superspace |
| topic | Combinatorics Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2412.17670 |