Geometry of Linear Diophantine equations

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Geometry of Linear Diophantine equations

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Title: Geometry of Linear Diophantine equations
Author: Kamalakshya Mahatab
Advisor: Amritanshu Prasad
Degree: M.Sc
Main Subjects: Mathematics
Institution: HBNI
Year: 2012
Pages: 58p.
Abstract: The non-negative solutions of linear homogeneous Diophantine equations are studied using the geometric theory of convex polytopes. After a brief introduction to the theory of convex polytopes and its relation to solutions of linear homogeneous Diophantine equations, a theorem of Stanley, Bruggesser and Mani on the decomposition of the monoid of solutions is discussed in detail. An application of this theorem, due to Stanley, to prove a conjecture of Anand, Dumir and Gupta is explained.
URI: http://hdl.handle.net/123456789/324

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