On the points-lines-planes conjecture

P. D. Seymour

doi:10.1016/0095-8956(82)90054-5

On the points-lines-planes conjecture

P. D. Seymour

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

10 Scopus citations

Abstract

It has been conjectured that in any matroid, if W₁, W₂, W₃ denote the number of points, lines, and planes respectively, then W₂² ≥ W₁W₃. We prove this conjecture (and some strengthenings) for matroids in which no line has five or more points, thus generalizing a result of Stonesifer, who proved it for graphic matroids.

Original language	English (US)
Pages (from-to)	17-26
Number of pages	10
Journal	Journal of Combinatorial Theory, Series B
Volume	33
Issue number	1
DOIs	https://doi.org/10.1016/0095-8956(82)90054-5
State	Published - Aug 1982
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Access to Document

10.1016/0095-8956(82)90054-5

Cite this

@article{b14cd65449284741b0b13ab7be5bde2b,

title = "On the points-lines-planes conjecture",

abstract = "It has been conjectured that in any matroid, if W1, W2, W3 denote the number of points, lines, and planes respectively, then W22 ≥ W1W3. We prove this conjecture (and some strengthenings) for matroids in which no line has five or more points, thus generalizing a result of Stonesifer, who proved it for graphic matroids.",

author = "Seymour, {P. D.}",

year = "1982",

month = aug,

doi = "10.1016/0095-8956(82)90054-5",

language = "English (US)",

volume = "33",

pages = "17--26",

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

issn = "0095-8956",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - On the points-lines-planes conjecture

AU - Seymour, P. D.

PY - 1982/8

Y1 - 1982/8

N2 - It has been conjectured that in any matroid, if W1, W2, W3 denote the number of points, lines, and planes respectively, then W22 ≥ W1W3. We prove this conjecture (and some strengthenings) for matroids in which no line has five or more points, thus generalizing a result of Stonesifer, who proved it for graphic matroids.

AB - It has been conjectured that in any matroid, if W1, W2, W3 denote the number of points, lines, and planes respectively, then W22 ≥ W1W3. We prove this conjecture (and some strengthenings) for matroids in which no line has five or more points, thus generalizing a result of Stonesifer, who proved it for graphic matroids.

UR - http://www.scopus.com/inward/record.url?scp=0040363085&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040363085&partnerID=8YFLogxK

U2 - 10.1016/0095-8956(82)90054-5

DO - 10.1016/0095-8956(82)90054-5

M3 - Article

AN - SCOPUS:0040363085

SN - 0095-8956

VL - 33

SP - 17

EP - 26

JO - Journal of Combinatorial Theory, Series B

JF - Journal of Combinatorial Theory, Series B

IS - 1

ER -

On the points-lines-planes conjecture

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this