Kamalakshya Mahatab
Geometry of Linear Diophantine equations - 2012 - 58p.
2012
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.
Mathematics
Diophantine Equations Geometry of Solutions HBNI MSc 8
HBNI MSc8
Geometry of Linear Diophantine equations - 2012 - 58p.
2012
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.
Mathematics
Diophantine Equations Geometry of Solutions HBNI MSc 8
HBNI MSc8