The Number of Solutions to Linear Diophantine Equations and Multivariate Splines
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Publication:3801631
DOI10.2307/2001089zbMath0655.10013OpenAlexW4251668311MaRDI QIDQ3801631
Wolfgang Dahmen, Charles A. Micchelli
Publication date: 1988
Full work available at URL: https://doi.org/10.2307/2001089
number of solutionsinteger linear programminglinear diophantine equationspolyhedral splinesnumber of magic squaresSylvester's denumerants
Integer programming (90C10) Combinatorial aspects of matroids and geometric lattices (05B35) Spline approximation (41A15) Arithmetic functions; related numbers; inversion formulas (11A25) Diophantine equations in many variables (11D72) Linear Diophantine equations (11D04)
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Cites Work
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- B-splines from parallelepipeds
- Linear Diophantine equations and local cohomology
- Translates of multivariate splines
- Subdivision algorithms for the generation of box spline surfaces
- A combinatorial distribution problem
- On the local linear independence of translates of a box spline
- On the Solution of Certain Systems of Partial Difference Equations and Linear Dependence of Translates of Box Splines
- On Multivariate B-Splines
- Interpolated Denumerants and Lambert Series
- Combinatorics and commutative algebra