The automorphism group of the random poset does not admit a generic pair

TL;DR

This paper investigates the automorphism group of the random poset, demonstrating that the conjugacy class of any pair of automorphisms is meager, thus addressing a question in the field.

Contribution

It proves that no pair of automorphisms of the random poset has a comeager conjugacy class, advancing understanding of the automorphism group's structure.

Findings

Conjugacy classes of automorphism pairs are meager

Addresses a question posed by Truss and Kuske-Truss

Provides insights into the topological dynamics of the automorphism group

Abstract

We show that the conjugacy class of every pair of automoprhisms of the random poset is meager. This answers a question of Truss; see also Kuske-Truss. EDIT. Work in progress, at the moment there is a gap in the proof of Theorem 2.