Uncountably many enumerations of well-quasi-ordered permutation classes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911613126180864 |
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| author | Brignall, Robert Vatter, Vincent |
| author_facet | Brignall, Robert Vatter, Vincent |
| contents | We construct an uncountable family of well-quasi-ordered permutation classes, each with a distinct enumeration sequence. This disproves a conjecture that all well-quasi-ordered permutation classes have algebraic generating functions, and in fact shows that many such classes lack D-finite or D-algebraic generating functions. Our construction is based on an uncountably large collection of factor-closed, well-quasi-ordered binary languages due to Pouzet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_12397 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Uncountably many enumerations of well-quasi-ordered permutation classes Brignall, Robert Vatter, Vincent Combinatorics We construct an uncountable family of well-quasi-ordered permutation classes, each with a distinct enumeration sequence. This disproves a conjecture that all well-quasi-ordered permutation classes have algebraic generating functions, and in fact shows that many such classes lack D-finite or D-algebraic generating functions. Our construction is based on an uncountably large collection of factor-closed, well-quasi-ordered binary languages due to Pouzet. |
| title | Uncountably many enumerations of well-quasi-ordered permutation classes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2211.12397 |