PreprintarXiv licencearXiv
Column Number of Delta-modular matrices: Refined Analysis via Sauer Matrices
Abstract
In this paper, we build upon the analysis initiated by Gennadiy Averkov and Matthias Schymura (2022) and establish that the number of distinct columns of a Δ-modular matrix A ∈ ℤm × n of rank m is O(m3 Δ). This upper bound was previously known only for odd values of Δ. Recall that a matrix is called Δ-modular if the maximum of the absolute values of its m × m minors equals Δ.
Related
- REFINED MODULAR SYMBOLS AND REFINED EISENSTEIN IDEALS
- A note on near alternating sign matrices with prescribed row and column weights
- Valuated delta matroids and principal minors of Hermitian matrices
- On the lower bound of the refined Bessis--Moussa--Villani conjecture: proof of the cases S_{6,3} and S_{7,3} for 3x3 matrices
- Montesinos Knots with Delta-Unknotting Number One
BibTeX
@misc{pribytkova2026column,
title = {{Column Number of Delta-modular matrices: Refined Analysis via Sauer Matrices}},
author = {Elizaveta Pribytkova and Dmitry Gribanov and Stanislav Moiseev},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.06215},
eprint = {2608.06215},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.06215},
}
RIS
TY - UNPB
TI - Column Number of Delta-modular matrices: Refined Analysis via Sauer Matrices
AU - Elizaveta Pribytkova
AU - Dmitry Gribanov
AU - Stanislav Moiseev
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.06215
UR - https://arxiv.org/abs/2608.06215
AB - In this paper, we build upon the analysis initiated by Gennadiy Averkov and Matthias Schymura (2022) and establish that the number of distinct columns of a Δ-modular matrix A ∈ ℤ^m × n of rank m is O(m^3 Δ). This upper bound was previously known only for odd values of Δ. Recall that a matrix is called Δ-modular if the maximum of the absolute values of its m × m minors equals Δ.
ER -