On the number of extension closed additive subcategories for uniformly oriented An quivers
Abstract
We provide a recurrence for computing the terms of the OEIS sequence A393920, introduced in 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.
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