Sparse solutions of linear Diophantine equations
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Sparse solutions of linear Diophantine equations

  • Author(s): Aliev, Iskander
  • De Loera, Jesus A.
  • Oertel, Timm
  • O'Neill, Christopher
  • et al.

Published Web Location

https://arxiv.org/pdf/1602.00344.pdf
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Abstract

We present structural results on solutions to the Diophantine system $A{\boldsymbol y} = {\boldsymbol b}$, ${\boldsymbol y} \in \mathbb Z^t_{\ge 0}$ with the smallest number of non-zero entries. Our tools are algebraic and number theoretic in nature and include Siegel's Lemma, generating functions, and commutative algebra. These results have some interesting consequences in discrete optimization.

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