Dmitry V. Gribanov

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Let A be an (m × n) integral matrix, and let P = {x : Ax ≤ b} be an n-dimensional polytope. The width of P is defined as w(P) = min{x ∈ Z n \ {0} : max x∈P x ⊤ u − min x∈P x ⊤ v}. Let ∆(A) and δ(A) denote the greatest and the smallest absolute values of a determinant among all r(A) × r(A) sub-matrices of A, where r(A) is the rank of a matrix A. We prove(More)
Let A be an m × n integral matrix of rank n. We say that A has bounded minors if the maximum of the absolute values of the n × n minors is at most k, where k is a some natural constant. We will call that matrices like k-modular. We investigate an integer program max{cx : Ax ≤ b, x ∈ Z n } where A is k-modular. We say that A is almost unimodular (see [2, 5])(More)
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