Visual characterization of associative quasitrivial nondecreasing operations on finite chains

TL;DR

This paper visually characterizes associative and bisymmetric quasitrivial nondecreasing operations on finite chains, providing new insights into their structure and estimating their quantity.

Contribution

It introduces visual characterizations for these operations and estimates their number, advancing understanding of their properties on finite chains.

Findings

Visual characterization of associative quasitrivial nondecreasing operations

Characterization of bisymmetric quasitrivial nondecreasing operations

Estimation of the number of such functions

Abstract

In this paper we provide visual characterization of associative quasitrivial nondecreasing operations on finite chains. We also provide a characterization of bisymmetric quasitrivial nondecreasing binary operations on finite chains. Finally, we estimate the number of functions belonging to the previous classes.