The Closure Operator of es-Splitting Matroids

TL;DR

This paper characterizes the closure operator and flats of es-splitting binary matroids, a generalization of graph splitting operations, in terms of the original matroid's properties.

Contribution

It provides a detailed description of the closure operator and flats of es-splitting matroids based on the original binary matroid, advancing understanding of their structure.

Findings

Closure operator of es-splitting matroids characterized

Flats of es-splitting matroids characterized

Generalization of graph splitting operation

Abstract

The es-splitting operation for binary matroids is a natural generalization of Slater's n-line splitting operation on graphs. In this paper, we characterize the closure operator of the es-splitting binary matroid $M^e_X$ in terms of the closure operator of the original binary matroid $M$. We also characterize the flats of the es-splitting binary matroid $M^e_X$ in terms of the flats of the original binary matroid $M$.