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Download fileKinser Inequalities and Related Matroids
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posted on 2021-11-13, 11:17 authored by Cameron, AmandaKinser developed a hierarchy of inequalities dealing with the dimensions of certain spaces constructed from a given quantity of subspaces. These inequalities can be applied to the rank function of a matroid, a geometric object concerned with dependencies of subsets of a ground set. A matroid which is representable by a matrix with entries from some finite field must satisfy each of the Kinser inequalities. We provide results on the matroids which satisfy each inequality and the structure of the hierarchy of such matroids.
History
Copyright Date
2013-01-01Date of Award
2013-01-01Publisher
Te Herenga Waka—Victoria University of WellingtonRights License
Author Retains CopyrightDegree Discipline
MathematicsDegree Grantor
Te Herenga Waka—Victoria University of WellingtonDegree Level
MastersDegree Name
Master of ScienceVictoria University of Wellington Item Type
Awarded Research Masters ThesisLanguage
en_NZVictoria University of Wellington School
School of Mathematics, Statistics and Operations ResearchAdvisors
Mayhew, DillonUsage metrics
Keywords
MatroidsRepresentabilityRank inequalitiesSchool: School of Mathematics, Statistics and Operations Research010107 Mathematical Logic, Set Theory, Lattices and Universal AlgebraMarsden: 230101 Mathematical Logic, set Theory, Lattices and CombinatoricsDegree Discipline: MathematicsDegree Level: MastersDegree Name: Master of ScienceMathematical Logic, Set Theory, Lattices and Universal Algebra