On functions with a unique identification minor

TL;DR

This paper explores functions with a unique identification minor, identifying new classes such as those determined by the order of first occurrence, and provides examples with small arity.

Contribution

It introduces a new class of functions with a unique identification minor based on the order of first occurrence, expanding understanding beyond 2-set-transitive functions.

Findings

2-set-transitive functions have a unique identification minor

Functions determined by order of first occurrence also have this property

Examples of such functions with small arity are provided

Abstract

We shed some new light to the problem of characterizing those functions of several arguments that have a unique identification minor. The 2-set-transitive functions are known to have this property. We describe another class of functions that have a unique identification minor, namely functions determined by the order of first occurrence. We also present some examples of other kinds of functions with a unique identification minor. These examples have a relatively small arity.