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