Sparse paving matroids, basis-exchange properties, and cyclic flats

Details Sparse paving matroids, basis-exchange properties, and cyclic flats Sparse paving matroids, basis-exchange properties, and cyclic flats

2010-11-03

arxiv.org/abs/1011.1010v1

Mathematics

Combinatorics

11 pages

Scientific paper

We provide evidence for five long-standing, basis-exchange conjectures for
matroids by proving them for the enormous class of sparse paving matroids. We
also explore the role that these matroids may play in the following problem: as
a function of the size of the ground set, what is the greatest number of cyclic
flats that a matroid can have?

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