English

Polynomials over structured grids

Combinatorics 2023-11-17 v1 Commutative Algebra Number Theory

Abstract

We study multivariate polynomials over `structured' grids. We begin by proposing an interpretation as to what it means for a finite subset of a field to be structured; we do so by means of a numerical parameter, the nullity. We then extend several results--notably, the Combinatorial Nullstellensatz and the Coefficient Theorem--to polynomials over structured grids. The main point is that the structure of a grid allows the degree constraints on polynomials to be relaxed.

Keywords

Cite

@article{arxiv.2110.05616,
  title  = {Polynomials over structured grids},
  author = {Bogdan Nica},
  journal= {arXiv preprint arXiv:2110.05616},
  year   = {2023}
}