Separating symmetric polynomials over finite fields
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917935674556416 |
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| author | Lopatin, Artem Martins, Pedro Antonio Muniz Lima, Lael Viana |
| author_facet | Lopatin, Artem Martins, Pedro Antonio Muniz Lima, Lael Viana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Separating symmetric polynomials over finite fields Lopatin, Artem Martins, Pedro Antonio Muniz Lima, Lael Viana Commutative Algebra Combinatorics Rings and Algebras 13A50, 12E20 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. |
| title | Separating symmetric polynomials over finite fields |
| topic | Commutative Algebra Combinatorics Rings and Algebras 13A50, 12E20 |
| url | https://arxiv.org/abs/2401.03318 |