Exponential valuations on lattice polygons valued at formal power series
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916991031312384 |
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| author | Boroczky, Karoly J. Domokos, Matyas Freyer, Ansgar Haberl, Christoph Li, Jin |
| author_facet | Boroczky, Karoly J. Domokos, Matyas Freyer, Ansgar Haberl, Christoph Li, Jin |
| contents | We classify valuations on lattice polygons with values in the ring of formal power series that commute with the action of the affine unimodular group. A typical example of such valuations is induced by the Laplace transform, but as it turns out there are many more. The classification is done in terms of formal power series that satisfy certain functional equations. We align our classification with the decomposition into so-called dilative components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04544 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential valuations on lattice polygons valued at formal power series Boroczky, Karoly J. Domokos, Matyas Freyer, Ansgar Haberl, Christoph Li, Jin Metric Geometry We classify valuations on lattice polygons with values in the ring of formal power series that commute with the action of the affine unimodular group. A typical example of such valuations is induced by the Laplace transform, but as it turns out there are many more. The classification is done in terms of formal power series that satisfy certain functional equations. We align our classification with the decomposition into so-called dilative components. |
| title | Exponential valuations on lattice polygons valued at formal power series |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2510.04544 |