English

Sparse solutions of linear Diophantine equations

Optimization and Control 2018-08-15 v3 Commutative Algebra Combinatorics

Abstract

We present structural results on solutions to the Diophantine system Ay=bA{\boldsymbol y} = {\boldsymbol b}, yZ0t{\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.

Keywords

Cite

@article{arxiv.1602.00344,
  title  = {Sparse solutions of linear Diophantine equations},
  author = {Iskander Aliev and Jesus A. De Loera and Timm Oertel and Christopher O'Neill},
  journal= {arXiv preprint arXiv:1602.00344},
  year   = {2018}
}
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