Smallest posets with given cyclic automorphism group

TL;DR

This paper determines the smallest size of posets that have a specified cyclic automorphism group of order n, for all n ≥ 1, establishing minimal examples for each cyclic group.

Contribution

It provides the exact minimal number of points in posets with a given cyclic automorphism group, a problem previously unresolved for all n.

Findings

Exact minimal sizes of posets for each cyclic automorphism group

Complete classification of smallest posets with cyclic symmetry

New bounds and constructions for posets with specified automorphisms

Abstract

For each $n\ge 1$ we determine the minimum number of points in a poset with cyclic automorphism group of order $n$.