Markov numbers of semigroups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913042777767936 |
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| author | Karpenkov, Oleg Ma, Yefei |
| author_facet | Karpenkov, Oleg Ma, Yefei |
| contents | In this paper, we systematically study generalized Markov numbers arising from semigroups of reduced integer matrices. This construction allows us to find these numbers by counting perfect matchings of a new family of bipartite graphs, which we call wug-snake graphs. We also show how this relates to the geometry of numbers and the classical theory of Markov minima. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17069 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Markov numbers of semigroups Karpenkov, Oleg Ma, Yefei Combinatorics Number Theory 11J06, 05C70, 11J70, 20M20 In this paper, we systematically study generalized Markov numbers arising from semigroups of reduced integer matrices. This construction allows us to find these numbers by counting perfect matchings of a new family of bipartite graphs, which we call wug-snake graphs. We also show how this relates to the geometry of numbers and the classical theory of Markov minima. |
| title | Markov numbers of semigroups |
| topic | Combinatorics Number Theory 11J06, 05C70, 11J70, 20M20 |
| url | https://arxiv.org/abs/2604.17069 |