Dependence of functions on their variables

Abstract

In this note I present a readable version of the proof of my 2001 result, giving a sufficient and necessary condition for a function on a combinatorial cube to essentially (locally) depend on at most one variable (see the end of the paper for the motivation), as well as some limiting results.

7 pages. This note will not be submitted for publication, but it will be included in the upcoming revised version of my 2000 monograph `Analytic quotients'