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arXiv · 2607.03029

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

Carmen Amarra·Alice Devillers·Cheryl E. Praeger
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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.

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Carmen Amarra, Alice Devillers, Cheryl E. Praeger. 2026-07-03. Recursive constructions for block-transitive, poset-imprimitive two-designs. https://arxiv.org/abs/2607.03029

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