The minimal arity of near-unanimity polymorphisms

TL;DR

This paper provides a simplified, explicit construction and proof for relational structures that admit near-unanimity polymorphisms with large minimal arity, nearly matching known upper bounds.

Contribution

It introduces a simplified, explicit construction and a self-contained proof for structures with high minimal arity near-unanimity polymorphisms.

Findings

Constructed structures with large minimal arity near-unanimity polymorphisms

Provided a simplified, explicit construction method

Achieved bounds close to known upper limits

Abstract

Dmitriy Zhuk has proved that there exist relational structures which admit near-unanimity polymorphisms, but the minimum arity of such a polymorphism is large and almost matches the known upper bounds. We present a simplified and explicit construction of such structures and a detailed, self-contained proof.