The Redei-Berge Hopf algebra of digraphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909146032373760 |
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| author | Grujić, Vladimir Stojadinović, Tanja |
| author_facet | Grujić, Vladimir Stojadinović, Tanja |
| contents | In a series of recent talks Richard Stanley introduced a symmetric function associated to digraphs called the Redei-Berge symmetric function. This symmetric function enumerates descent sets of permutations corresponding to digraphs. We show that such constructed symmetric function arises from a suitable structure of combinatorial Hopf algebra on digraphs. The induced Redei-Berge polynomial satisfies the deletion-contraction property which makes it similar to the chromatic polynomial. The Berge's classical result on the number of Hamiltonian paths in digraphs is a consequence of the reciprocity formula for the Redei-Berge polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07606 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Redei-Berge Hopf algebra of digraphs Grujić, Vladimir Stojadinović, Tanja Combinatorics 05C20, 16T30, 05E05 In a series of recent talks Richard Stanley introduced a symmetric function associated to digraphs called the Redei-Berge symmetric function. This symmetric function enumerates descent sets of permutations corresponding to digraphs. We show that such constructed symmetric function arises from a suitable structure of combinatorial Hopf algebra on digraphs. The induced Redei-Berge polynomial satisfies the deletion-contraction property which makes it similar to the chromatic polynomial. The Berge's classical result on the number of Hamiltonian paths in digraphs is a consequence of the reciprocity formula for the Redei-Berge polynomial. |
| title | The Redei-Berge Hopf algebra of digraphs |
| topic | Combinatorics 05C20, 16T30, 05E05 |
| url | https://arxiv.org/abs/2402.07606 |