D. Gribanov

activity

20242026

collaborators

5 papers

math.CO2026

Column Number of Delta-modular matrices: Refined Analysis via Sauer Matrices

Elizaveta Pribiytkova, Dmitry Gribanov

In this paper, we build upon the analysis initiated by Gennadiy Averkov \& Matthias Schymura (2022) and establish that the number of distinct columns of a $Δ$ -modular matrix $A \in…

cs.CC2026

Hyperplanes Avoiding Problem and Integer Points Counting in Polyhedra

Grigorii Dakhno, Dmitry Gribanov, Nikita Kasianov +4

In our work, we consider the problem of computing a vector $x \in Z^{n}$ of minimum $∥ \cdot ∥_{p}$ -norm such that $a^{⊤} x \neq = a_{0}$ , for any vector $(a, a_{0})$ from a given subset of…

cs.DM2025

Diagonal Frobenius Number via Gomory's Relaxation and Discrepancy

Dmitry Gribanov, Dmitry Malyshev, Panos Pardalos

For a matrix $A \in Z^{k \times n}$ of rank $k$ , the diagonal Frobenius number $F_{diag} (A)$ is defined as the minimum $t \in Z_{\geq 1}$ , such that, for any $b \in \text{sp…

math.CO2025

On the Vertices of Delta-modular Polyhedra

Bludov Mikhail, Gribanov Dmitry, Klimenko Maxim +4

Let $P$ be a polytope defined by the system $A x \leq b$ , where $A \in R^{m \times n}$ , $b \in R^{m}$ , and $rank (A) = n$ . We give a short geometric proof of the following tigh…

cs.DS2024

A New and Faster Representation for Counting Integer Points in Parametric Polyhedra

D. Gribanov, D. Malyshev, P. Pardalos +1

In this paper, we consider the counting function $E_{P} (y) = ∣ P_{y} \cap Z^{n_{x}} ∣$ for a parametric polyhedron $P_{y} = {x \in R^{n_{x}} : A x \leq b + B y}$ , where $y \in R^{n_…