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arXiv · 2401.03318

Separating symmetric polynomials over finite fields

Artem Lopatin·Pedro Antonio Muniz Martins·Lael Viana Lima
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Abstract

The set $S(n)$ of all elementary symmetric polynomials in $n$ variables is a minimal generating set for the algebra of symmetric polynomials in $n$ variables, but over a finite field ${\mathbb F}_q$ the set $S(n)$ is not a minimal separating set for symmetric polynomials in general. We determined when $S(n)$ is a minimal separating set for the algebra of symmetric polynomials having the least possible number of elements.

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Artem Lopatin, Pedro Antonio Muniz Martins, Lael Viana Lima. 2025-02-15. Separating symmetric polynomials over finite fields. https://doi.org/10.46298/cm.14627

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