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arXiv · 2511.06555

Companion matrices, permutations and lattice ideals

Nsibiet E. Udo·Praise Adeyemo
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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.

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Nsibiet E. Udo, Praise Adeyemo. 2025-11-09. Companion matrices, permutations and lattice ideals. https://arxiv.org/abs/2511.06555

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