{"title":"A Nearly Finitary Matroid that is not $k$-Nearly Finitary","authors":"Patrick Tam","doi":"10.37236/10467","DOIUrl":null,"url":null,"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 $k \\in \\mathbb{N}$.","PeriodicalId":509530,"journal":{"name":"The Electronic Journal of Combinatorics","volume":" 39","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Electronic Journal of Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37236/10467","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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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 $k \in \mathbb{N}$.
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