Small Matrices with Small Inverses: Unimodular Zerofree Cases
Combinatorics
2026-05-13 v3 Discrete Mathematics
Number Theory
Abstract
We consider unimodular matrices such that neither nor contain zero entries. Matrices typically exhibit a trade-off: small imply large . We investigate rare cases where both remain small, classify these matrices up to symmetry, and discuss aspects of this balanced setting.
Keywords
Cite
@article{arxiv.2605.03691,
title = {Small Matrices with Small Inverses: Unimodular Zerofree Cases},
author = {Steven Finch},
journal= {arXiv preprint arXiv:2605.03691},
year = {2026}
}
Comments
11 pages; proof of 2x2 counting formula (Euler totient-based) and more empirical results in Addendum