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# Kinser Inequalities and Related Matroids

thesis

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

2013-01-01## Date of Award

2013-01-01## Publisher

Te Herenga Waka—Victoria University of Wellington## Rights License

Author Retains Copyright## Degree Discipline

Mathematics## Degree Grantor

Te Herenga Waka—Victoria University of Wellington## Degree Level

Masters## Degree Name

Master of Science## Victoria University of Wellington Item Type

Awarded Research Masters Thesis## Language

en_NZ## Victoria University of Wellington School

School of Mathematics, Statistics and Operations Research## Advisors

Mayhew, Dillon## Usage 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

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