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Abstract
We consider 2designs which admit a group of automorphisms that is flagtransitive and leaves invariant a chain of nontrivial pointpartitions. We build on our recent work on 2designs which are blocktransitive but not necessarily flagtransitive. In particular we use the concept of the “array” of a point subset with respect to the chain of pointpartitions; the array describes the distribution of the points in the subset among the classes of each partition. We obtain necessary and sufficient conditions on the array in order for the subset to be a block of such a design. By explicit construction we show that for any s≥2, there are infinitely many 2designs admitting a flagtransitive group that preserves an invariant chain of pointpartitions of length s. Moreover an exhaustive computer search, using Magma, seeking designs with e_{1}e_{2}e_{3} points (where each e_{i}≤50) and a partition chain of length s=3, produced 57 such flagtransitive designs, among which only three designs arise from our construction—so there is still much to learn.
Original language  English 

Journal  Designs, Codes, and Cryptography 
DOIs  
Publication status  Published  20 Apr 2024 
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 1 Finished

Exceptionally symmetric combinatorial designs
ARC Australian Research Council
3/12/20 → 2/12/23
Project: Research