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On Matroid And Polymatroid Connectivity, Dennis Wayne Hall Ii

LSU Doctoral Dissertations

Matroids were introduced in 1935 by Hassler Whitney to provide a way to abstractly capture the dependence properties common to graphs and matrices. One important class of matroids arises by taking as objects some finite collection of one-dimensional subspaces of a vector space. If, instead, one takes as objects some finite collection of subspaces of dimensions at most k in a vector space, one gets an example of a k-polymatroid.

Connectivity is a pivotal topic of study in the endeavor to understand the structure of matroids and polymatroids. In this dissertation, we study the notion of connectivity from several …