The Automorphism Conjecture for Ordered Sets of Width $\leq 11$

TL;DR

This paper proves the automorphism conjecture for ordered sets with width up to 11, supporting the idea that many automorphisms arise from products of automorphisms on symmetric parts.

Contribution

It extends the automorphism conjecture proof to ordered sets of width ≤ 11, advancing understanding of automorphism structures in combinatorics.

Findings

Automorphism conjecture proven for width ≤ 11 ordered sets

Supports the meta conjecture on automorphism composition

Highlights the role of symmetric subsets in automorphism structure

Abstract

We prove the automorphism conjecture for ordered sets of width less than or equal to 11. The proof supports the meta conjecture that a large number of automorphisms is achievable only as some type of product of independent automorphisms on highly symmetric subsets.