In linear programming, a Hilbert basis is a minimal set of integer vectors
such that
every integer vector in its convex cone

is also in its integer cone
.
In other words, if an integer vector is a non-negative combination of vectors in a
Hilbert basis, then this vector is also in the integer non-negative combination of vectors in the Hilbert basis.
References
- Carathéodory bounds for integer cones [1]
- An Integer Analogue of Carathéodory's Theorem [2]
- A Counterexample to an Integer Analogue of Carathéodory's Theorem [3]
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