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On a Simple Connection Between Δ-modular ILP and LP, and a New Bound on the Number of Integer Vertices
[article]

2022
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arXiv
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pre-print

Let A ∈ Z^m × n, rank(A) = n, b ∈ Z^m, and P be an n-dimensional polyhedron, induced by the system A x ≤ b. It is a known fact that if F is a k-face of P, then there exist at least n-k linearly independent inequalities of the system A x ≤ b that become equalities on F. In other words, there exists a set of indices J, such that |J| = n-k, rank(A_JC) = n-k, and A_J x - b_J = 0, for any x ∈ F. We show that a similar fact holds for the integer polyhedron P_I = conv(P ∩ Z^n) if we additionally

arXiv:2203.03907v1
fatcat:6vh7vbinzff6ti525r6keemd6m