# Characterizations of quasitrivial symmetric nondecreasing associative operations

## TL;DR

This paper characterizes a class of n-ary operations on chains that are quasitrivial, symmetric, nondecreasing, and associative, and explores the equivalence of associativity and bisymmetry in this context, including finite chains.

## Contribution

It provides a comprehensive description of these operations and shows that associativity can be replaced by bisymmetry, extending understanding of their algebraic structure.

## Key findings

- Characterization of quasitrivial symmetric nondecreasing associative operations
- Equivalence of associativity and bisymmetry in this class
- Analysis of finite chain cases

## Abstract

We provide a description of the class of n-ary operations on an arbitrary chain that are quasitrivial, symmetric, nondecreasing, and associative. We also prove that associativity can be replaced with bisymmetry in the definition of this class. Finally we investigate the special situation where the chain is finite.