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Linjär algebrans tenikers användningsområden inom kombinatorik
KTH, School of Engineering Sciences (SCI).
2019 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Linear algebras techniques use in combinatorics (English)
Abstract [sv]

Matematiken innehåller flera svåra problem. I den här artikeln undersöker vi hur en del av dessa problem kan lösas med hjälp av tekniker från andra matematikdiscipliner än problemens egna. Först löser vi en del kombinatorik-problem genom att utnyttja att maximala antalet linjärt oberoende vektorer i F^n är n. Sedan diskuterar vi samt förklarar hur Z.Dvirs bevis rörande ändliga kakeyamängder. Han lyckas hitta en undre begränsning för kakeyamängder med hjälp av polynom.

Abstract [en]

Mathematics contains many hard problems. In this paper we discuss how some of these hard problems can be solved with techniques from other math fields than the problems own discipline. First we solve some combinatorial problems using the knowledge that a maximum amount of vectors in a linearly independent set over a subset of a vector space F^n over a field F is n. Then we discuss and explain Z.Dvir's famous proof regarding Kakeya sets over finite fields. He is able to establish a lower bound of the size of Kakeya sets using polynomials.

 

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:118
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-254715OAI: oai:DiVA.org:kth-254715DiVA, id: diva2:1334842
Supervisors
Examiners
Available from: 2019-07-03 Created: 2019-07-03 Last updated: 2019-07-03Bibliographically approved

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CiteExportLink to record
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  • apa
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