Additive decomposition schemes for polynomial functions over fields


Miguel Couceiro, Erkko Lehtonen, Tamás Waldhauser




The authors' previous results on the arity gap of functions of several variables are refined by considering polynomial functions over arbitrary fields. We explicitly describe the polynomial functions with arity gap at least $3$, as well as the polynomial functions with arity gap equal to $2$ for fields of characteristic $0$ or $2$. These descriptions are given in the form of decomposition schemes of polynomial functions.