New Hereditary and Mutation-Invariant Properties Arising from Forks
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913210541539328 |
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| author | Ervin, Tucker J. |
| author_facet | Ervin, Tucker J. |
| contents | A hereditary property of quivers is a property preserved by restriction to any full subquiver. Similarly, a mutation-invariant property of quivers is a property preserved by mutation. Using forks, a class of quivers developed by M. Warkentin, we introduce a new hereditary and mutation-invariant property. We prove that a quiver being mutation-equivalent to a finite number of non-forks -- defined as having a finite forkless part -- is this new property, using only elementary methods. Additionally, we show that a more general property -- having a finite pre-forkless part -- is also a new hereditary and mutation-invariant property in much the same manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07502 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New Hereditary and Mutation-Invariant Properties Arising from Forks Ervin, Tucker J. Combinatorics 05E40 A hereditary property of quivers is a property preserved by restriction to any full subquiver. Similarly, a mutation-invariant property of quivers is a property preserved by mutation. Using forks, a class of quivers developed by M. Warkentin, we introduce a new hereditary and mutation-invariant property. We prove that a quiver being mutation-equivalent to a finite number of non-forks -- defined as having a finite forkless part -- is this new property, using only elementary methods. Additionally, we show that a more general property -- having a finite pre-forkless part -- is also a new hereditary and mutation-invariant property in much the same manner. |
| title | New Hereditary and Mutation-Invariant Properties Arising from Forks |
| topic | Combinatorics 05E40 |
| url | https://arxiv.org/abs/2306.07502 |