Work

Block-transitive designs with a poset of imprimitive partitions

Year: 2026

Type: article

Abstract: We study block designs which admit an automorphism group that is transitive on blocks and points, and leaves invariant every partition in a given finite poset of partitions of the point set. The full stabiliser G of all the partitions in the poset is a generalised wreath product. We use the theory of generalised wreath products to give necessary and sufficient conditions, in terms of the ‘array’ of a point-subset B , for the set of G -images of B to form the block-set of a G -block-transitive 2-design. This generalises previous results for the special cases where the poset is a chain or an anti-chain. We also give explicit infinite families of examples of 2-designs for each poset involving three proper partitions, and for the famous N -poset with four partitions. (Posets with two proper partitions have been treated previously.) This suggests the problem of finding explicit examples for other posets.

Source: Designs Codes and Cryptography

DOI: 10.1007/s10623-026-01891-1

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

Institutions: University of the Philippines Diliman, The University of Western Australia

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Australian Research Council