On Rota's conjecture and excluded minors containing large projective geometries

被引:16
作者
Geelen, J [1 ]
Gerards, B
Whittle, G
机构
[1] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada
[2] CWI, NL-1090 GB Amsterdam, Netherlands
[3] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands
[4] Victoria Univ Wellington, Sch Math & Comp Sci, Wellington, New Zealand
基金
加拿大自然科学与工程研究理事会;
关键词
matroids; Rota's conjecture; excluded minors;
D O I
10.1016/j.jctb.2005.09.005
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove that an excluded minor for the class of GF(q)-representable matroids cannot contain a large projective geometry over GF(q) as a minor. (C) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码:405 / 425
页数:21
相关论文
共 11 条
  • [1] Artin E., 1957, GEOMETRIC ALGEBRA
  • [2] A SIMPLE THEOREM ON 3-CONNECTIVITY
    BIXBY, RE
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1982, 45 (JUN) : 123 - 126
  • [3] Brualdi R. A., 1969, Bulletin of the Australian Mathematical Society, V1, P161, DOI DOI 10.1017/S000497270004140X
  • [4] The excluded minors for GF(4)-representable matroids
    Geelen, JF
    Gerards, AMH
    Kapoor, A
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2000, 79 (02) : 247 - 299
  • [5] GEELEN JF, 2003, 034 VICT U WELL SCH
  • [6] DEPENDENCE GRAPH FOR BASES IN MATROIDS
    KROGDAHL, S
    [J]. DISCRETE MATHEMATICS, 1977, 19 (01) : 47 - 59
  • [7] On inequivalent representations of matroids over finite fields
    Oxley, J
    Vertigan, D
    Whittle, G
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 1996, 67 (02) : 325 - 343
  • [8] Oxley J., 1993, MATROID THEORY
  • [9] CONNECTIVITY IN MATROIDS
    TUTTE, WT
    [J]. CANADIAN JOURNAL OF MATHEMATICS, 1966, 18 (06): : 1301 - &
  • [10] MENGERS THEOREM FOR MATROIDS
    TUTTE, WT
    [J]. JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS SECTION B-MATHEMATICS AND MATHEMATICAL, 1965, B 69 (1-2): : 49 - +