TL;DR
This paper establishes a fundamental relationship between the volume and the minimal generating set size (rank) of lattices, showing that the rank cannot increase faster than the volume, which has implications for lattice theory.
Contribution
It proves a new bound linking the rank of lattices to their volume, providing insight into the structure of lattices in higher dimensions.
Findings
Rank of lattices is bounded by their volume.
The minimal generating set size cannot grow faster than volume.
Provides a new theoretical limit in lattice theory.
Abstract
We show the rank (i.e. minimal size of a generating set) of lattices cannot grow faster than the volume.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Mathematical Dynamics and Fractals