Pith. sign in

REVIEW 1 cited by

Matroids over hyperfields

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1601.01204 v5 pith:PFJV4IJJ submitted 2016-01-06 math.CO math.AGmath.RA

Matthew Baker , Nathan Bowler This is my paper · ORCID
classification math.COmath.AGmath.RA
keywords matroidscallhyperfieldsmatroidnotionsstrongweakalgebraic
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We present an algebraic framework which simultaneously generalizes the notion of linear subspaces, matroids, valuated matroids, and oriented matroids. We call the resulting objects matroids over hyperfields. In fact, there are (at least) two natural notions of matroid in this context, which we call weak and strong matroids. We give "cryptomorphic" axiom systems for such matroids in terms of circuits, Grassmann-Plucker functions, and dual pairs, and establish some basic duality theorems. We also show that if F is a doubly distributive hyperfield then the notions of weak and strong matroid over F coincide.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the borderline of fields and hyperfields, part II -- Enumeration and classification of the hyperfields of order 7

    math.RA 2024-12 conditional novelty 6.0 of 10

    There are exactly 277 seven-element hyperfields, all built on the cyclic multiplicative group of order six, and the paper classifies which of them arise as quotients of fields.

Pith tools