English

Dependence of functions on their variables

Combinatorics 2025-03-12 v1 Logic

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.

Keywords

Cite

@article{arxiv.2503.07864,
  title  = {Dependence of functions on their variables},
  author = {Ilijas Farah},
  journal= {arXiv preprint arXiv:2503.07864},
  year   = {2025}
}

Comments

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'

R2 v1 2026-06-28T22:14:54.746Z