Title

Semi-magic squares, permutation matrices and constant line-sum matrices

Date of Publication

2000

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Abstract/Summary

This thesis is based mainly on Sections 1 to 6 of the article entitled Marriage, Magic and Solitaire by David Leep and Gerry Myerson (1999). Motivated by a non-losing solitaire game, the main part of this thesis begins by explaining how the Hall's Marriage Theorem applies to the solitaire game. It proceeds by approaching the solitaire game problem from the point of view of semi-magic squares. This approach provides a second way of proving the solitaire game. This is followed up with a discussion of permutation matrices, the simplest nonzero semi-magic squares. This thesis proves a theorem concerning permutation matrices as building blocks of semi-magic squares. Finally, the concept of permutation matrices and semi-magic squares is generalized to constant line-sum matrices over an arbitrary field.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU09580

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

86 leaves

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