A Generalization of the Greene-Kleitman Duality Theorem

TL;DR

This paper extends the Greene-Kleitman duality theorem for posets, providing a more general framework that unifies classical and recent local versions, with implications for discrete solitons.

Contribution

It introduces a broader generalization of the Greene-Kleitman duality theorem, connecting classical and recent local versions through a unified approach.

Findings

Proves a generalized duality theorem for posets.

Links classical and local duality results.

Provides a new approach aligned with classical methods.

Abstract

In this paper, we describe and prove a generalization of both the classical Greene-Kleitman duality theorem for posets and the local version proved recently by Lewis-Lyu-Pylyavskyy-Sen in studying discrete solitons, using an approach more closely linked to the approach of the classical case.