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

2010/11/03 by Joseph E. Bonin, Bonin, Joseph E.
Computer Science · Mathematics · #05B35 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1011.1010

openalex publication_date 2010/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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?

Citations

• On the structure of the h-vector of a paving matroid

Related

• A Method to construct the Sparse-paving Matroids over a Finite Set
• Enumerating matroids of fixed rank
• White's Conjecture for Paving Matroids
• On the number of matroids compared to the number of sparse paving matroids
• Counterexamples to two conjectures about matroids