Perfect matroids over hyperfields

Nathan Bowler, Rudi A. Pendavingh

Research output: Contribution to journalArticleAcademic

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Abstract

A hyperfield $H$ is stringent if $a\boxplus b$ is a singleton unless $a=-b$, for all $a,b\in H$. By a construction of Marc Krasner, each valued field gives rise to a stringent hyperfield. We show that if $H$ is a stringent skew hyperfield, then weak matroids over $H$ are strong matroids over $H$. Also, we present vector axioms for matroids over stringent skew hyperfields which generalize the vector axioms for oriented matroids and valuated matroids.
Original languageEnglish
Article number1908.03420vl
Number of pages16
JournalarXiv.org, e-Print Archive, Mathematics
Publication statusPublished - 9 Aug 2019

Bibliographical note

16 pages

Keywords

  • math.CO
  • 05B35, 52C40

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