Squarefree polynomials with prescribed coefficients
Amotz Oppenheim, Mark Shusterman

TL;DR
This paper proves that for large enough finite fields, one can select coefficients from specified subsets to construct squarefree polynomials, under certain size conditions of these subsets.
Contribution
It establishes the existence of squarefree polynomials with prescribed coefficients from subsets of finite fields, extending previous results to broader subset size conditions.
Findings
Existence of squarefree polynomials with prescribed coefficients in finite fields
Conditions on subset sizes ensuring such polynomials exist
Generalization of prior results to larger subset size regimes
Abstract
For nonempty subsets of a (large enough) finite field satisfying we show that there exist such that is a squarefree polynomial.
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