Quadratic Symmetric Polynomials and an analogue of the Davenport Constant

TL;DR

This paper introduces a new constant related to quadratic symmetric polynomials over finite fields, providing exact values and bounds, extending the classical Davenport constant concept.

Contribution

It defines the constant D(φ, p) for sequences on finite fields using quadratic symmetric polynomials and establishes its exact values and bounds.

Findings

Exact values of D(φ, p) determined for certain cases

Lower and upper bounds provided for the constant

Extension of Davenport constant concept to quadratic symmetric polynomials

Abstract

In this paper, we define the constant $D(\varphi, p)$, an analogue for the Davenport constant, for sequences on the finite field $\mathbb{F}_p$, defined via quadratic symmetric polynomials. Next, we state a series of results presenting either the exact value of $D(\varphi, p)$, or lower and upper bounds for this constant.