Symmetric polynomials over finite fields

2022/11/15 by M. Domokos, Domokos, Mátyás, Botond Miklósi +1
Computer Science · Engineering · Mathematics · #13A50 (Primary) 12E20 (Secondary) #Coding theory and cryptography #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2211.08124

openalex publication_date 2022/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 p^k,2p^k,…,(q-1)p^k, 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.

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