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Golden-Mean and Secret Sharing Matroids

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thesis
posted on 10.11.2021, 23:05 by Welsh, Michael

Maximum-sized results are an important part of matroid theory, and results currently exist for various classes of matroids. Archer conjectured that the maximum-sized golden-mean matroids fall into three distinct classes, as op- posed to the one class of all current results. We will prove a partial result that we hope will lead to a full proof. In the second part of this thesis, we look at secret sharing matroids, with a particular emphasis on the class of group-induced p-representable matroids, as introduced by Matúš. We give new proofs for results of Matúš', relating to M(K₄), F₇ and F⁻₇. We show that the techniques used do not extend in some natural ways, and pose some unanswered questions relating to the structure of secret sharing matroids.

History

Copyright Date

01/01/2011

Date of Award

01/01/2011

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