The Closure Operator of es-Splitting Matroids

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 $M_X^e$ in terms of the closure operator of the original binary matroid $M$. We also characterize the flats of the es-splitting binary matroid $M_X^e$ in terms of the flats of the original binary matroid $M$.