The Closure Operator, Flats and Hyperplanes of es-Splitting Matroid

The es-splitting operation on 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 describe the ats and the hyperplanes of the es-splitting bi- nary matroid M^e_X in terms of the ats and the hyperplanes, respectively of the original binary matroid M.