Matroids with an infinite circuit-cocircuit intersection

Nathan Bowler; Johannes Carmesin

doi:10.1016/j.jctb.2014.02.005

Matroids with an infinite circuit-cocircuit intersection

Nathan Bowler, Johannes Carmesin

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	78-91
Journal	Journal of Combinatorial Theory. Series B
Volume	107
Early online date	13 Mar 2014
DOIs	https://doi.org/10.1016/j.jctb.2014.02.005
Publication status	Published - Jul 2014

Keywords

math.CO
05C63, 05B35
infinite matroid
tame
duality
representability

Access to Document

10.1016/j.jctb.2014.02.005Licence: None: All rights reserved

https://www.sciencedirect.com/science/article/pii/S0095895614000148Licence: None: All rights reserved

Cite this

@article{a26974e09c744ecfb89f54f6393b7446,

title = "Matroids with an infinite circuit-cocircuit intersection",

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. ",

keywords = "math.CO, 05C63, 05B35, infinite matroid, tame, duality, representability",

author = "Nathan Bowler and Johannes Carmesin",

year = "2014",

month = jul,

doi = "10.1016/j.jctb.2014.02.005",

language = "English",

volume = "107",

pages = "78--91",

journal = "Journal of Combinatorial Theory. Series B",

issn = "0095-8956",

publisher = "Elsevier",

}

TY - JOUR

T1 - Matroids with an infinite circuit-cocircuit intersection

AU - Bowler, Nathan

AU - Carmesin, Johannes

PY - 2014/7

Y1 - 2014/7

N2 - 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.

AB - 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.

KW - math.CO

KW - 05C63, 05B35

KW - infinite matroid

KW - tame

KW - duality

KW - representability

U2 - 10.1016/j.jctb.2014.02.005

DO - 10.1016/j.jctb.2014.02.005

M3 - Article

SN - 0095-8956

VL - 107

SP - 78

EP - 91

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

ER -

Matroids with an infinite circuit-cocircuit intersection

Abstract

Keywords

Access to Document

Fingerprint

Cite this