A Method to construct the Sparse-paving Matroids over a Finite Set

Abstract

In this work we present an algorithm to construct sparse-paving matroids over finite set $S$. From this algorithm we derive some useful bounds on the cardinality of the set of circuits of any Sparse-Paving matroids which allow us to prove in a simple way an asymptotic relation between the class of Sparse-paving matroids and the whole class of matroids. Additionally we introduce a matrix based method which render an explicit partition of the $r$-subsets of $S$, $\left(\genfrac{}{}{0ex}{}{S}{r}\right)={\bigsqcup }_{i=1}^{\gamma }{\mathcal{U}}_i$ such that each ${\mathcal{U}}_i$ defines a sparse-paving matroid of rank $r$.

Preprint

References in corpus (3)

• Sparse paving matroids, basis-exchange properties, and cyclic flats
• On the structure of the h-vector of a paving matroid
• An entropy argument for counting matroids

Cited by in corpus (1)

• A Method to construct all the Paving Matroids over a Finite Set