Nsibiet E. Udo | Searcharxiv

arXiv2025

Companion matrices, permutations and lattice ideals

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.

math.AC↗

arXiv2024

Ideals, representations and a symmetrised Bernoulli triangle

We study some representations of symmetric groups arising from a certain ideal in the coordinate ring of affine n-space. Our results give graded and representation-theoretic enhancements of sequence 337 of the Online Encyclopaedia of Integer Sequences, involving a symmetric version of the Bernoulli triangle.

math.AC↗