๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On Weak Maps of Ternary Matroids

โœ Scribed by J Oxley; G Whittle

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
181 KB
Volume
19
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

โœฆ Synopsis

Let M and N be ternary matroids having the same rank and the same ground set, and assume that every independent set in N is also independent in M. The main result of this paper proves that if M is 3-connected and N is connected and non-binary, then M = N . A related result characterizes precisely when a matroid that is obtained by relaxing a circuit-hyperplane of a ternary matroid is also ternary.

๐Ÿ“œ SIMILAR VOLUMES

Weak Maps and Stabilizers of Classes of
Weak Maps and Stabilizers of Classes of Matroids
โœ James Geelen; James Oxley; Dirk Vertigan; Geoff Whittle ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 338 KB

Let F be a field and let N be a matroid in a class N N of F-representable matroids that is closed under minors and the taking of duals. Then N is an F-stabilizer for N N if every representation of a 3-connected member of N N is determined up to elementary row operations and column scaling by a repre

A Characterization of the Orientations o
A Characterization of the Orientations of Ternary Matroids
โœ Jon Lee; Matt Scobee ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 280 KB

A matroid or oriented matroid is dyadic if it has a rational representation with all nonzero subdeterminants in [ \2 k : k # Z]. Our main theorem is that an oriented matroid is dyadic if and only if the underlying matroid is ternary. A consequence of our theorem is the recent result of G. Whittle th

On Circuit Valuation of Matroids
On Circuit Valuation of Matroids
โœ Kazuo Murota; Akihisa Tamura ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 257 KB

The concept of valuated matroids was introduced by Dress and Wenzel as a quantitative extension of the base exchange axiom for matroids. This paper gives several sets of cryptomorphically equivalent axioms of valuated matroids in terms of R โˆช -โˆž -valued vectors defined on the circuits of the underly

On matroid separations of graphs
On matroid separations of graphs
โœ Klaus Truemper ๐Ÿ“‚ Article ๐Ÿ“… 1987 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 308 KB

Let K be a connected and undirected graph, and M be the polygon matroid of K . Assume that, for some k 2 1, the matroid M is kseparable and k-connected according to the matroid separability and connectivity definitions of W. T. Tutte. In this paper we classify the matroid kseparations of M in terms