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Polynomials over structured grids

Part of: Algebraic combinatorics Real and complex fields Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  04 October 2022

Bogdan Nica
Bogdan Nica*
Affiliation:
Department of Mathematical Sciences, Indiana University–Purdue University, Indianapolis, IN, USA
*
Email: bnica@iu.edu
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Abstract

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.

Keywords

Combinatorial Nullstellensatzstructured gridnullity

MSC classification

Primary: 05E40: Combinatorial aspects of commutative algebra
Secondary: 11T06: Polynomials 12D10: Polynomials

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 32 , Issue 2 , March 2023 , pp. 284 - 298
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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