# The sum of matroids I

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## Abstract

Let **M** _{1} = (*S*, **F** _{1}), **M** _{2} = (*S*, **F** _{2}),..., **M** _{ k } = (*S*, **F** _{ k }) be *k* matroids on the same underlying set *S*. We define the *sum* (or *union*) of these matroids to be the matroid on the same set *S* with * X* ⊆

*S*independent if and only if

**X**can be decomposed as

*X*

_{1}∪

*X*

_{2}∪ ... ∪

*X*

_{ k }where

*X*

_{1}∈

**F**

_{1},

*X*

_{2}∈

**F**

_{2},...,

*X*

_{ k }∈

**F**

_{ k }.

## Keywords

Rank Function Span Forest Matroid Partition Matroid Intersection Problem Electric Network Theory
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1989