PreprintarXiv licencearXiv
On the number of cokernel-closed additive subcategories for uniformly oriented An quivers
Abstract
We study the integer sequence that enumerates cokernel-closed, idempotent split, full, additive subcategories of the category of finite dimensional complex representations of a uniformly oriented An quiver. Using a combinatorial model, we describe a non-obvious connection of this sequence to Catalan numbers and derive an implicit recurrence. We also describe some basic properties of the lattice underlying the sequences, in particular, we give an explicit description of the meet irreducible elements of that lattice.
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BibTeX
@misc{mazorchuk2026number,
title = {{On the number of cokernel-closed additive subcategories for uniformly oriented $A_n$ quivers}},
author = {Volodymyr Mazorchuk and Shuoyang Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07999},
eprint = {2610.07999},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07999},
}
RIS
TY - UNPB
TI - On the number of cokernel-closed additive subcategories for uniformly oriented A_n quivers
AU - Volodymyr Mazorchuk
AU - Shuoyang Xu
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.07999
UR - https://arxiv.org/abs/2610.07999
AB - We study the integer sequence that enumerates cokernel-closed, idempotent split, full, additive subcategories of the category of finite dimensional complex representations of a uniformly oriented A_n quiver. Using a combinatorial model, we describe a non-obvious connection of this sequence to Catalan numbers and derive an implicit recurrence. We also describe some basic properties of the lattice underlying the sequences, in particular, we give an explicit description of the meet irreducible elements of that lattice.
ER -