The r-depth of a matroid

Silva, J. A. Dias da; Fonseca, Amélia

doi:10.1016/0012-365x(93)e0209-m

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Constructing a Fundamental Partition1

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Cited by 5 publications

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“…This process is much like a finding the so-called flag transversal for a sum of matroids [9]. It will be helpful to define the concept of a quasi-transversal which, like the transversal, is inspired from a matroid version [8].…”

Section: Constructing a Fundamental Partitionmentioning

confidence: 99%

An elementary, illustrative proof of the Rado–Horn theorem

Casazza¹,

Peterson²

2012

Linear Algebra and its Applications

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The Rado-Horn theorem provides necessary and sufficient conditions for when a family of vectors can be partitioned into a fixed number of linearly independent sets. Such partitions exist if and only if every subfamily of the vectors satisfies the so-called RadoHorn inequality. In this paper we provide an elementary proof of the Rado-Horn theorem as well as results for the redundant case. Previous proofs give no information about how to actually partition the vectors; we use ideas present in our proof to find subfamilies of vectors which may be used to construct a kind of "optimal" partition.Published by Elsevier Inc.

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Section: Constructing a Fundamental Partitionmentioning

confidence: 99%