Symmetric polynomials over finite fields

Domokos, Mátyás and Miklósi, Botond (2023) Symmetric polynomials over finite fields. FINITE FIELDS AND THEIR APPLICATIONS, 89. No-102224. ISSN 1071-5797

Preview

Text 1-s2.0-S1071579723000667-main.pdf Available under License Creative Commons Attribution Non-commercial No Derivatives. Download (389kB) | Preview

Abstract

It is shown that two vectors with coordinates in the finite q-element field of characteristic p belong to the same orbit under the natural action of the symmetric group if each of the elementary symmetric polynomials of degree pk , 2pk , . . . , (q − 1)pk , k = 0, 1, 2, . . . has the same value on them. This separating set of polynomial invariants for the natural permutation representation of the symmetric group is not far from being minimal when q = p and the dimension is large compared to p. A relatively small separating set of multisymmetric polynomials over the field of q elements is derived.

Actions (login required)

Edit Item