A coarse Tutte polynomial for hypermaps
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914906761068544 |
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| author | Ellis-Monaghan, Joanna A. Moffatt, Iain Noble, Steven |
| author_facet | Ellis-Monaghan, Joanna A. Moffatt, Iain Noble, Steven |
| contents | We give an analogue of the Tutte polynomial for hypermaps. This polynomial can be defined as either a sum over subhypermaps, or recursively through deletion-contraction reductions where the terminal forms consist of isolated vertices. Our Tutte polynomial extends the classical Tutte polynomial of a graph as well as the Tutte polynomial of an embedded graph (i.e., the ribbon graph polynomial), and it is a specialization of the transition polynomial via a medial map transformation. We give hypermap duality and partial duality identities for our polynomial, as well as some evaluations, and examine relations between our polynomial and other hypermap polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00194 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A coarse Tutte polynomial for hypermaps Ellis-Monaghan, Joanna A. Moffatt, Iain Noble, Steven Combinatorics 05C31 (primary) 05C65, 05C10 (secondary) We give an analogue of the Tutte polynomial for hypermaps. This polynomial can be defined as either a sum over subhypermaps, or recursively through deletion-contraction reductions where the terminal forms consist of isolated vertices. Our Tutte polynomial extends the classical Tutte polynomial of a graph as well as the Tutte polynomial of an embedded graph (i.e., the ribbon graph polynomial), and it is a specialization of the transition polynomial via a medial map transformation. We give hypermap duality and partial duality identities for our polynomial, as well as some evaluations, and examine relations between our polynomial and other hypermap polynomials. |
| title | A coarse Tutte polynomial for hypermaps |
| topic | Combinatorics 05C31 (primary) 05C65, 05C10 (secondary) |
| url | https://arxiv.org/abs/2404.00194 |