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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.07502 |
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Table of 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.