On the complex-representable excluded minors for real-representability

被引：0

作者：

Campbell, Rutger ^{[1
]}

Geelen, Jim ^{[1
]}

机构：

[1] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON, Canada

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES B | 2020年 / 143卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Matroid; Excluded minors; Representable matroids;

D O I：

10.1016/j.jctb.2019.11.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that each real-representable matroid is a minor of a complex-representable excluded minor for real-representability. More generally, for an infinite field F-1 and a field extension F-2, if F-1-representability is not equivalent to F-2-representability, then each F-1-representable matroid is a minor of a F-2-representable excluded minor for F-1-representability. (C) 2019 Published by Elsevier Inc.

引用

页码：16 / 28

页数：13

共 11 条

[1] [Anonymous], T AM MATH SOC
[2] Bjorner A., 1999, Oriented matroids
[3] Lattice path matroids: The excluded minors
Bonin, Joseph E.
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2010, 100 (06) : 585 - 599
[4] BRYLAWSKI TH, 1975, STUD APPL MATH, V54, P143
[5] Ingleton A. W., 1973, Journal of Combinatorial Theory, Series B, V15, P51, DOI 10.1016/0095-8956(73)90031-2
[6] Knuth D. E., 1974, Journal of Combinatorial Theory, Series A, V16, P398, DOI 10.1016/0097-3165(74)90063-6
[7] Lazarson T., 1958, J LOND MATH SOC, V33, P21
[8] Matus F., 2017, COMBINATORICA, DOI [10.1007/s00493-016-3534-, DOI 10.1007/S00493-016-3534-Y.]
[9] On excluded minors for real-representability
Mayhew, Dillon
Newman, Mike
Whittle, Geoff
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2009, 99 (04) : 685 - 689
[10] Almost all matroids are nonrepresentable
Nelson, Peter
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2018, 50 (02) : 245 - 248

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