A matroidal generalization of results of Drisko and Chappell

TL;DR

This paper generalizes existing matroid intersection results by proving that a collection of 2n-1 sets of size n in the intersection of two matroids guarantees a rainbow subset of size n, extending prior combinatorial theorems.

Contribution

It introduces a new matroidal generalization of previous results, expanding the understanding of rainbow sets in matroid intersections.

Findings

Any 2n-1 sets of size n in M ∩ N contain a rainbow set of size n

Generalizes results of Drisko and Chappell to broader matroid contexts

Provides new combinatorial bounds for matroid intersection problems

Abstract

Let $M$ and $N$ be two matroids on the same ground set. We generalize results of Drisko and Chapell by showing that any $2n-1$ sets of size $n$ in $M \cap N$ have a rainbow set of size $n$ in $M \cap N$.