SOME PROPERTIES OF MATROIDS OBTAINED FROM CONCEPT LATTICE APPROACHES

Hua Mao

doi:10.22342/jims.22.2.267.183-190

Abstract

Using the Hasse diagrams of concept lattices, we investigate therelations between matroids and geometric contexts, followed byjudging a mathematical construction to be a matroid. We provide anidea to find out the dual of a matroid from the ways of conceptlattice drawing. In addition, we utilize the Hasse diagrams ofconcept lattices to discuss the minors of matroids, direct sum ofmatroids and the connectivity of a matroid. All the consequences demonstrate that the theory of concept lattice drawing can be usedinto matroids. This generalizes the applied fields of conceptlattices.DOI : http://dx.doi.org/10.22342/jims.22.2.267.183-190

Highlights

Introduction and PreliminariesWe know from [8,14,16] that as a branch of combinatorics, a matroid is a structure that captures the generalizations of linear independence in vector spaces.2000 Mathematics Subject Classification: 05B35; 68R05; 06B75
Depending on the sophistication of the notion, it may be nontrivial to show that the different formulations are equivalent, a phenomenon sometimes called cryptomorphism significant definitions of a matroid include those in terms of independent sets, circuits, closed sets and hyperplanes
If we explore an approach to deal with matroids with the Hasse diagrams of concept lattices, using the assistance of matroid geometric representations, we may infer that some constructions and algorithms relative to matroids will be produced

Summary

Introduction

Introduction and PreliminariesWe know from [8,14,16] that as a branch of combinatorics, a matroid is a structure that captures the generalizations of linear independence in vector spaces.2000 Mathematics Subject Classification: 05B35; 68R05; 06B75. If we explore an approach to deal with matroids with the Hasse diagrams of concept lattices, using the assistance of matroid geometric representations (that is, using the assistance of the families of closed sets of matroids), we may infer that some constructions and algorithms relative to matroids will be produced. Using the relationships and ready-made algorithms for drawing concept lattices, we search out the methods to determining a construction to be a matroid.

Results

Conclusion