Quadratic symmetric polynomials and an analogue of the Davenport constant

Abstract

We define the constant $$ D(\varphi_F, p) $$ , 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 $$ D(\varphi_F, p) $$ , or lower and upper bounds for this constant.