Prime Factorization of Meanders
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866917534450581504 |
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| author | Belousov, Y. |
| author_facet | Belousov, Y. |
| contents | In this paper, we introduce a prime factorization of open meanders, articulated through the framework of 2-colored operads. We demonstrate that each open meander can be canonically constructed from building blocks of two types: iterated snakes and irreducible meanders. We find out that iterated snakes allow efficient enumeration, and thus the problem of enumerating meanders reduces to the problem of enumerating irreducible meanders. Additionally, we present some results concerning the asymptotic of meanders of both classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_10289 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Prime Factorization of Meanders Belousov, Y. Combinatorics 57K99, 05A99 In this paper, we introduce a prime factorization of open meanders, articulated through the framework of 2-colored operads. We demonstrate that each open meander can be canonically constructed from building blocks of two types: iterated snakes and irreducible meanders. We find out that iterated snakes allow efficient enumeration, and thus the problem of enumerating meanders reduces to the problem of enumerating irreducible meanders. Additionally, we present some results concerning the asymptotic of meanders of both classes. |
| title | Prime Factorization of Meanders |
| topic | Combinatorics 57K99, 05A99 |
| url | https://arxiv.org/abs/2112.10289 |