Dual matroid

In matroid theory, the dual of a matroid is another matroid that has the same elements as , and in which a set is independent if and only if has a…

Papers overview

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2016

Let $M=(E,\mathcal B)$ be an $\mathbb F_q$-linear matroid; denote by ${\mathcal B}$ the family of its bases, $s(M;\alpha)=\sum_{B…

2014

Matroids designs are defined to be matroids in which the hyperplanes all have the same size. The dual of a matroid design is a…

2012

We demonstrate that two key theorems of Amaldi et al. (Math Methods Oper Res 69:205–223, 2009), which they presented with rather…

2007

2004

ing from the behavior of linearly independent sets of columns of a matrix, in 1935, Whitney defined a matroid M to consist of a…

1997

Let M be a finite matroid with rank function r. We will write A ⊆ M when we mean that A is a subset of the ground set of M , and…

1974

Unified proofs of two theorems on fundamental transversal matroids are presented. A necessary condition for a matroid to be a…