English

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

Combinatorics 2024-12-12 v2

Abstract

The class of kk-nearly finitary matroids for some natural number kk 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 kk-nearly finitary for any kNk \in \mathbb{N}.

Keywords

Cite

@article{arxiv.2404.04721,
  title  = {A Nearly Finitary Matroid that is not $k$-Nearly Finitary},
  author = {Patrick Tam},
  journal= {arXiv preprint arXiv:2404.04721},
  year   = {2024}
}

Comments

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