Geometry of Linear Diophantine equations
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TextPublication details: 2012Description: 58pSubject(s): Mathematics | Diophantine Equations | Geometry of Solutions | HBNI MSc 8Online resources: Click here to access online Dissertation note: 2012M.ScHBNI 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.
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2012
M.Sc
HBNI
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.
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