New Hereditary and Mutation-Invariant Properties Arising from Forks
| Autor: | Ervin, Tucker J. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | The Electronic Journal of Combinatorics Volume 31, Issue 1 (2024), Article P1.16 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.37236/12167 |
| Popis: | 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. Comment: 30 pages, fixed typos |
| Databáze: | arXiv |
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