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Matroids with an infinite circuit-cocircuit intersection

2012/02/15 by Johannes Carmesin, Carmesin, Johannes, Nathan Bowler +1
Computer Science · Mathematics · #05B35 #05C63 #Advanced Algebra and Logic #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Topological and Geometric Data Analysis #math.CO #msc:05B35 #msc:05C63

paper · pdf · doi:10.48550/arxiv.1202.3406

openalex publication_date 2012/02/15 · arxiv created 2012/02/28 · arxiv updated 2012/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct some matroids that have a circuit and a cocircuit with infinite intersection. This answers a question of Bruhn, Diestel, Kriesell, Pendavingh and Wollan. It further shows that the axiom system for matroids proposed by Dress does not axiomatize all infinite matroids. We show that one of the matroids we define is a thin sums matroid whose dual isn't a thin sums matroid.

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