On the constant partial-dual polynomials of hypermaps
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915094501261312 |
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| author | Xiang, Yibing Yan, Qi |
| author_facet | Xiang, Yibing Yan, Qi |
| contents | In this paper, we introduce the partial-dual polynomial for hypermaps, extending the concept from ribbon graphs. We discuss the basic properties of this polynomial and characterize it for hypermaps with exactly one hypervertex containing a non-zero constant term. Additionally, we show that the partial-dual polynomial of a prime connected hypermap $H$ is constant if and only if $H$ is a plane hypermap with a single hyperedge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04178 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the constant partial-dual polynomials of hypermaps Xiang, Yibing Yan, Qi Combinatorics 05B35, 05C10, 05C31 In this paper, we introduce the partial-dual polynomial for hypermaps, extending the concept from ribbon graphs. We discuss the basic properties of this polynomial and characterize it for hypermaps with exactly one hypervertex containing a non-zero constant term. Additionally, we show that the partial-dual polynomial of a prime connected hypermap $H$ is constant if and only if $H$ is a plane hypermap with a single hyperedge. |
| title | On the constant partial-dual polynomials of hypermaps |
| topic | Combinatorics 05B35, 05C10, 05C31 |
| url | https://arxiv.org/abs/2501.04178 |