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


Affiliations

  • Dr. Vishwanath Karad MIT World Peace University, School of Mathematics and Statistics, Pune, 411038, India
  • Savitribai Phule Pune University, Department of Mathematics, Pune, 411007, India

Abstract

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 MeX 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 MeX in terms of the ats and the hyperplanes, respectively of the original binary matroid M.

Keywords

Binary Matroid, es-splitting operation, closure operator, ats, hyperplanes

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