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Binzhou Xia
Binzhou Xia
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Generators of the ringalgebra of symmetric polynomials over finite fields

Let $F$ be a finite field and $A$ be the ringalgebra of symmetric polynomials on $x_1,\dots,x_n$ over $F$. What is known about the generators of $A$ except the elementary symmetric polynomials? In particular, given some power sum polynomials, how to determine whether they generate $A$?

Generators of the ring of symmetric polynomials over finite fields

Let $F$ be a finite field and $A$ be the ring of symmetric polynomials on $x_1,\dots,x_n$ over $F$. What is known about the generators of $A$ except the elementary symmetric polynomials? In particular, given some power sum polynomials, how to determine whether they generate $A$?

Generators of the algebra of symmetric polynomials over finite fields

Let $F$ be a finite field and $A$ be the algebra of symmetric polynomials on $x_1,\dots,x_n$ over $F$. What is known about the generators of $A$ except the elementary symmetric polynomials? In particular, given some power sum polynomials, how to determine whether they generate $A$?

Source Link
Binzhou Xia
Binzhou Xia
  • 767
  • 4
  • 15

Generators of the ring of symmetric polynomials over finite fields

Let $F$ be a finite field and $A$ be the ring of symmetric polynomials on $x_1,\dots,x_n$ over $F$. What is known about the generators of $A$ except the elementary symmetric polynomials? In particular, given some power sum polynomials, how to determine whether they generate $A$?