Geometry of Linear Diophantine equations
Material type:
TextPublication details: 2012Description: 58pSubject(s): Online resources: 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.
THESIS & DISSERTATION
| Home library | Call number | Materials specified | URL | Status | Date due | Barcode | |
|---|---|---|---|---|---|---|---|
| IMSc Library | HBNI MSc8 (Browse shelf(Opens below)) | Link to resource | Available | 67513 |
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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