Companion matrices, permutations and lattice ideals
Commutative Algebra
2025-11-11 v1 Algebraic Geometry
Group Theory
Representation Theory
Abstract
This paper investigates a novel connection between reductions of companion matrices associated with a symmetric family of certain binomial ideals in the coordinate ring of affine n-space and permutation matrices. Specifically, for fixed monomial orders, we observe that the reduced companion matrices yield permutation matrices satisfying group-theoretic relations. We explore the implications of these reductions, their connections to lattice ideals, and characterize the groups generated by these transformations.
Keywords
Cite
@article{arxiv.2511.06555,
title = {Companion matrices, permutations and lattice ideals},
author = {Nsibiet E. Udo and Praise Adeyemo},
journal= {arXiv preprint arXiv:2511.06555},
year = {2025}
}
Comments
15 pages. An article by Nsibiet E. Udo and Praise Adeyemo; Appendix by NEU