New hereditary and mutation-invariant properties arising from forks
The electronic journal of combinatorics, Tome 31 (2024) no. 1
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.
@article{10_37236_12167,
author = {Tucker Ervin},
title = {New hereditary and mutation-invariant properties arising from forks},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {1},
doi = {10.37236/12167},
zbl = {1555.13024},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12167/}
}
Tucker Ervin. New hereditary and mutation-invariant properties arising from forks. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/12167
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