# Perfect matroids over hyperfields

Nathan Bowler, Rudi A. Pendavingh

## 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 language English 1908.03420vl 16 arXiv.org, e-Print Archive, Mathematics Published - 9 Aug 2019

16 pages

• math.CO
• 05B35, 52C40

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