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- W2968335093 abstract "We investigate valuated matroids with an additional algebraic structure on their residue matroids. We encode the structure in terms of representability over stringent hyperfields. A hyperfield $H$ is {em stringent} if $aboxplus b$ is a singleton unless $a=-b$, for all $a,bin H$. 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 the vectors of any weak matroid over $H$ are orthogonal to its covectors, and we deduce that 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." @default.
- W2968335093 created "2019-08-22" @default.
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- W2968335093 date "2019-08-09" @default.
- W2968335093 modified "2023-09-27" @default.
- W2968335093 title "Perfect matroids over hyperfields" @default.
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