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Nica, Bogdan
2023.
On an identity of Sylvester.
Expositiones Mathematicae,
Vol. 41,
Issue. 4,
p.
125511.
Published online by Cambridge University Press: 04 October 2022
We study multivariate polynomials over ‘structured’ grids. Firstly, we propose 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.