Modulus for bases of matroids
arXiv:2404.05650
The paper investigates the modulus of the family of bases in matroids, linking it to concepts such as strength, fractional arboricity, and principal partitions, introducing Beurling sets, revisiting Edmonds's base packing and covering theorems, and establishing duality and a full description of p‑modulus for all p.
Abstract
In this work, we explore the application of modulus in matroid theory, specifically, the modulus of the family of bases of matroids. This study not only recovers various concepts in matroid theory, including the strength, fractional arboricity, and principal partitions, but also offers new insights. In the process, we introduce the concept of a Beurling set. Additionally, our study revisits and provides an alternative approach to two of Edmonds's theorems related to the base packing and base covering problems. This is our stepping stone for establishing Fulkerson modulus duality for the family of bases. Finally, we provide a relationship between the base modulus of matroids and their dual matroids, and a complete understanding of the base -modulus across all values of .