Degree Type

Creative Component

Semester of Graduation

Spring 2018

Department

Mathematics

First Major Professor

Sung Yell Song

Second Major Professor

Leslie Hogben

Third Major Professor

Steve Butler

Degree(s)

Master of Science (MS)

Major(s)

Mathematics

Abstract

The permanent of an $n\times n$ matrix $A=(a_{i j})$ with real entries is defined by the sum $$\sum_{\sigma \in S_n} \prod_{i=1}^{n} a_{i \sigma(i)}$$ where $S_n$ denotes the symmetric group on the $n$-element set $\{1,2,\dots,n\}$. In this creative component we survey some known properties of permanents, calculation of permanents for particular types of matrices and their applications in combinatorics and linear algebra. Then we follow the lines of van Lint's exposition of Egorychev's proof for the van der Waerden's conjecture on the permanents of doubly stochastic matrices. The purpose of this component is to provide elementary proofs of several interesting known facts related to permanents of some special matrices. It is an expository survey paper in nature and reports no new findings.

Comments

Program of Study Committee:

Sung Yell Song, Major Professor

Steve Butler

Jonas Hartwig

Leslie Hogben

Copyright Owner

Vicente Valle Martinez

File Format

application/pdf

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