On the number of extension closed additive subcategories for uniformly oriented $A_n$ quivers

Volodymyr Mazorchuk

On the number of extension closed additive subcategories for uniformly oriented $A_n$ quivers

Representation Theory 2026-07-01 v1 Combinatorics

Authors: Volodymyr Mazorchuk

Abstract

We provide a recurrence for computing the terms of the OEIS sequence A393920, introduced in \cite{KS}. We also describe a surprising connection between A393920 and the Fibonacci sequence A000045, obtain non-trivial lower and upper exponential bounds for its growth, and investigate connections with partial orders, Catalan numbers, and convex topologies on finite chains. For the representation-theoretic lattice underlying A393920, we describe its atoms, coatoms, join-irreducible and meet-irreducible elements.

Keywords

extension closed subcategories additive subcategories quiver representations OEIS sequence Fibonacci sequence partial orders Catalan numbers convex topologies

Cite

@article{arxiv.2607.00651,
  title  = {On the number of extension closed additive subcategories for uniformly oriented $A_n$ quivers},
  author = {Volodymyr Mazorchuk},
  journal= {arXiv preprint arXiv:2607.00651},
  year   = {2026}
}