Papers › On the Maximal Number of Columns of a Δ-modular Integer Matrix: Bounds and Computations
On the Maximal Number of Columns of a Δ-modular Integer Matrix: Bounds and Computations
Gennadiy Averkov, Matthias Schymura
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We study the maximal number of pairwise distinct columns in a Δ-modular integer matrix with m rows. Recent results by Lee et al. provide an asymptotically tight upper bound of O(m²) for fixed Δ. We complement this and obtain an upper bound of the form O(Δ) for fixed m, and with the implied constant depending polynomially on m.
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