Monotonic Mappings Invariant Linearisation of Finite Posets

TL;DR

This paper introduces a new method to convert any finite poset into a linear order while preserving the original order and extending monotonic mappings, facilitating analysis and application of order-preserving functions.

Contribution

The paper presents a novel procedure for linearising finite posets that maintains original orderings and extends monotonic mappings to the linearised structure.

Findings

Preserves original ordering in the linearisation process

Allows extension of monotonic and antitonic mappings

Enables analysis of posets through linear orderings

Abstract

In this paper we describe a novel a procedure to build a linear order from an arbitrary poset which (i) preserves the original ordering and (ii) allows to extend monotonic and antitonic mappings defined over the original poset to monotonic and antitonic mappings over the new linear poset.