非 $k$ 近似有限 Matroid

The Electronic Journal of Combinatorics Pub Date : 2024-02-09 DOI:10.37236/10467

Patrick Tam

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摘要

某个自然数 $k$ 的 $k$ 近似有限母题类是近乎有限母题类的一个子类。一个自然的问题是这个包含是否恰当。我们通过构造一个对于任意 $k 在 \mathbb{N}$ 中都不是 $k$ 近似有限的 matroid 来肯定地回答这个问题。

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

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 $k \in \mathbb{N}$.

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The Electronic Journal of Combinatorics

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