Sparse solutions of linear diophantine equations

Aliev I, De Loera JA, Oertel T, O'Neill C (2017)

Publication Type: Journal article

Publication year: 2017

Journal

SIAM Journal on Applied Algebra and Geometry Society for Industrial and Applied Mathematics (SIAM)

Book Volume: 1

Pages Range: 239-253

Journal Issue: 1

DOI: 10.1137/16M1083876

Abstract

We present structural results on solutions to the Diophantine system Ay = b, y ∈ Z^t≥0 that have the smallest number of nonzero 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.

Authors with CRIS profile

Timm Oertel Professur für Mathematische Analyse von Daten (Data Analytics)

Involved external institutions

Cardiff University

United Kingdom (GB) University of California Davis (UCDAVIS)

United States (USA) (US)

How to cite

APA:

Aliev, I., De Loera, J.A., Oertel, T., & O'Neill, C. (2017). Sparse solutions of linear diophantine equations. SIAM Journal on Applied Algebra and Geometry, 1(1), 239-253. https://dx.doi.org/10.1137/16M1083876

MLA:

Aliev, Iskander, et al. "Sparse solutions of linear diophantine equations." SIAM Journal on Applied Algebra and Geometry 1.1 (2017): 239-253.

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