A Nearly Finitary Matroid that is not $k$-Nearly Finitary

Abstract

The class of $k$-nearly finitary matroids for some natural number $k$ is a subclass of the class of nearly finitary matroids. A natural question is whether this inclusion is proper. We answer this question affirmatively by constructing a nearly finitary matroid that is not $k$-nearly finitary for any $k\in \mathbb{N}$.

5 pages, Electronic Journal of Combinatorics 31(1) (2024) #P1.32 Proof of Theorem 5 (2.1) was revised a bit in this latest postprint