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Integer programming regards optimization problems, where one seeks to find integer values for a set of unknowns, that optimizes the objective function. A common subset of this type of problems are integer linear programming problems, where all inequalities, equalities and the objective function are linear in the unknowns.
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Is a Parametric Integer Linear Programming Problem eventually quasi-polynomial?
I will consider a family of Integer Linear Programs parametrized by a positive integer $t$.
Let $\mathbf{x} = (x_1, \ldots, x_n)$ be the indeterminates.
Let $A$ an $m$ by $n$ matrix whose elements a …