Uniform random posets

TL;DR

This paper introduces a simple Markov chain-based algorithm for generating labeled posets that approximates a uniform distribution, with convergence in total variation, enabling more uniform sampling of posets.

Contribution

It presents a novel Markov chain algorithm for almost uniform generation of labeled posets, improving sampling methods in combinatorics.

Findings

The algorithm converges in total variation to the uniform distribution.

It efficiently generates labeled posets of specified size.

The method is simple and based on directed acyclic graphs.

Abstract

We propose a simple algorithm generating labelled posets of given size according to the almost uniform distribution. By "almost uniform" we understand that the distribution of generated posets converges in total variation to the uniform distribution. Our method is based on a Markov chain generating directed acyclic graphs.