Rota's basis conjecture for matroids with density close to one

被引：0
|
作者：
McGuinness, Sean [1 ]
机构：
[1] Thompson Rivers Univ, Kamloops, BC, Canada
来源：
ADVANCES IN APPLIED MATHEMATICS | 2024年 / 152卷
关键词：
Matroid; Basis; Rota's basis conjecture; Girth; LATIN SQUARES; ALON-TARSI;
D O I：
10.1016/j.aam.2023.102593
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Rota's basis conjecture (RBC) states that given a collection 13 of n bases in a matroid M of rank n, one can always find n disjoint rainbow bases with respect to 13. We show that if M is a matroid having n + k elements, then one can construct n - k3 disjoint rainbow bases.& COPY; 2023 Elsevier Inc. All rights reserved.
引用
收藏
页数：27
相关论文
共 50 条
  • [11] Girth Conditions and Rota’s Basis Conjecture
    Benjamin Friedman
    Sean McGuinness
    Graphs and Combinatorics, 2023, 39
  • [12] Wide partitions, Latin tableaux, and Rota's basis conjecture
    Chow, TY
    Fan, CK
    Goemans, MX
    Vondrak, J
    ADVANCES IN APPLIED MATHEMATICS, 2003, 31 (02) : 334 - 358
  • [13] REDUCTION OF ROTA'S BASIS CONJECTURE TO A PROBLEM ON THREE BASES
    Chow, Timothy Y.
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2009, 23 (01) : 369 - 371
  • [14] Rota's basis conjecture holds for random bases of vector spaces
    Sauermann, Lisa
    EUROPEAN JOURNAL OF COMBINATORICS, 2024, 121
  • [15] Stability, fragility, and Rota's Conjecture
    Mayhew, Dillon
    Whittle, Geoff
    van Zwam, Stefan H. M.
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 2012, 102 (03) : 760 - 783
  • [16] Sticky matroids and Kantor's Conjecture
    Hochstattler, Winfried
    Wilhelmi, Michael
    ALGEBRA UNIVERSALIS, 2019, 80 (01)
  • [17] Sticky matroids and Kantor’s Conjecture
    Winfried Hochstättler
    Michael Wilhelmi
    Algebra universalis, 2019, 80
  • [18] Branch-width and Rota's conjecture
    Geelen, J
    Whittle, G
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 2002, 86 (02) : 315 - 330
  • [19] The odd case of Rota's bases conjecture
    Aharoni, Ron
    Loebl, Martin
    ADVANCES IN MATHEMATICS, 2015, 282 : 427 - 442
  • [20] Roudneff's Conjecture for Lawrence Oriented Matroids
    Montejano, Luis Pedro
    Alfonsin, Jorge Luis Ramirez
    ELECTRONIC JOURNAL OF COMBINATORICS, 2015, 22 (02):
12345