Companion matrices, permutations and lattice ideals
arXiv:2511.06555
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.
15 pages. An article by Nsibiet E. Udo and Praise Adeyemo; Appendix by NEU