Linear function of a poset
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918004669808640 |
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| author | Mitrovic, Stefan |
| author_facet | Mitrovic, Stefan |
| contents | Stanley and Grinberg introduced a symmetric function associated with digraphs and named it the Redei-Berge symmetric function. This function arises from a suitable combinatorial Hopf algebra on digraphs, which made it possible to assign the Redei-Berge function to posets. In this paper, we define a new combinatorial Hopf algebra of posets whose character is a close cousin of the Redei-Berge character for posets. Further, we investigate the properties of the symmetric function that arises from this algebra and explore its expansions in various natural bases of $QSym$ and $Sym$. Finally, we obtain an interesting method for decomposing a poset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20975 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear function of a poset Mitrovic, Stefan Combinatorics Stanley and Grinberg introduced a symmetric function associated with digraphs and named it the Redei-Berge symmetric function. This function arises from a suitable combinatorial Hopf algebra on digraphs, which made it possible to assign the Redei-Berge function to posets. In this paper, we define a new combinatorial Hopf algebra of posets whose character is a close cousin of the Redei-Berge character for posets. Further, we investigate the properties of the symmetric function that arises from this algebra and explore its expansions in various natural bases of $QSym$ and $Sym$. Finally, we obtain an interesting method for decomposing a poset. |
| title | Linear function of a poset |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2504.20975 |