Totally free expansions of matroids.

DOI10.1006/jctb.2001.2068zbMath1048.05020OpenAlexW1990357453MaRDI QIDQ1850582

Dirk Vertigan, James F. Geelen, James G. Oxley, Geoffrey P. Whittle

Publication date: 10 December 2002

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/5fcf5e138466bda2ef6b5ec17ff6d68732386e54

zbMATH Keywords

cloneinequivalent representations3-connected matroidstotally free matroid

Mathematics Subject Classification ID

Combinatorial aspects of matroids and geometric lattices (05B35)

Related Items (18)

Inequivalent representations of matroids having no \(U_{3,6}\)-minor ⋮ Enumerating orientations of the free spikes ⋮ Confinement of matroid representations to subsets of partial fields ⋮ Inequivalent representations of matroids over prime fields ⋮ Clones in 3-connected frame matroids ⋮ A Matroid Extension Result ⋮ The templates for some classes of quaternary matroids ⋮ A note on totally free matroids ⋮ The structure of the 3-separations of 3-connected matroids ⋮ Clonal sets in \(GF(q)\)-representable matroids ⋮ A note on clone sets in representable matroids ⋮ Representable orientations of the free spikes ⋮ On clone sets of \(GF(q)\)-representable matroids ⋮ A short proof of non-GF(5)-representability of matroids ⋮ Matroids Denser than a Projective Geometry ⋮ Recent work in matroid representation theory ⋮ Generalized \(\Delta\text{--}Y\) exchange and \(k\)-regular matroids ⋮ Obstacles to decomposition theorems for sixth-root-of-unity matroids

Cites Work

• On relative position in extensions of combinatorial geometries
• Decomposition of regular matroids
• Matroid representation over GF(3)
• A simple theorem on 3-connectivity
• A note on the non-spanning circuits of a matroid
• On Reid's characterization of the ternary matroids
• A characterization of certain excluded-minor classes of matroids
• On weak maps of ternary matroids
• Weak maps and stabilizers of classes of matroids
• Stabilizers of classes of representable matroids
• On the structure of 3-connected matroids and graphs
• The smallest rounded sets of binary matroids
• Generalized \(\Delta\text{--}Y\) exchange and \(k\)-regular matroids
• The excluded minors for GF(4)-representable matroids
• A characterisation of the matroids representable over GF(3) and the rationals
• On inequivalent representations of matroids over finite fields
• On the Uniqueness of Matroid Representations Over GF(4)
• Single-element extensions of matroids
• Connectivity in Matroids
• On Matroids Representable over 𝐺𝐹(3) and Other Fields
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