Recursive constructions for block-transitive, poset-imprimitive two-designs

Carmen Amarra; Alice Devillers; Cheryl E. Praeger

Recursive constructions for block-transitive, poset-imprimitive two-designs

Combinatorics 2026-07-03 v1

Authors: Carmen Amarra , Alice Devillers , Cheryl E. Praeger

Abstract

We give two general constructions for $2$ -designs, that can be used recursively, and interchangeably, to produce new infinite families of $2$ -designs admitting block-transitive groups of automorphisms which preserve arbitrarily large posets of partitions of the point-set. The only arbitrarily large posets for which constructions were previously known are chains of arbitrary length. Using the constructions we exhibit new infinite families of poset-imprimitive block-transitive $2$ -designs corresponding to several different arbitrarily large posets, as well as constructions for most posets with four nodes.

Cite

@article{arxiv.2607.03029,
  title  = {Recursive constructions for block-transitive, poset-imprimitive two-designs},
  author = {Carmen Amarra and Alice Devillers and Cheryl E. Praeger},
  journal= {arXiv preprint arXiv:2607.03029},
  year   = {2026}
}