Work

On the Column Number of Delta-Modular Matrices: an $O(m^2 Δ)$ Bound via the Shifted Heller Constant

Year: 2026

Type: preprint

Abstract: In this paper, we build on the analysis initiated by Averkov and Schymura (2022) and prove that the shifted Heller constant for matrices with $m$ rows is at most $m^2 + m$ for all sufficiently large $m$. Consequently, the number of distinct columns of a $Δ$-modular matrix $A \in Z^{m \times n}$ of rank $m$ is at most $O(m^2 Δ)$. This improves upon the earlier bounds of $O(m^4 Δ)$ and $O(m^2 Δ^2)$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.06215

Authors: Pribytkova, Elizaveta, Gribanov, Dmitrii, Taletskii, Dmitrii, Moiseev, Stanislav

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Moscow Institute of Physics and Technology

OpenAlex ID: W7201866564

Cites: 8

Cited by: 1

Related to: 10