Delandtsheer--Doyen parameters for block-transitive point-imprimitive 2-designs
Abstract
Delandtsheer and Doyen bounded, in terms of the block size, the number of points of a point-imprimitive, block-transitive 2-design. To do this they introduced two integer parameters, m and n, now called Delandtsheer--Doyen parameters, linking the block size with the parameters of an associated imprimitivity system on points. We show that the Delandtsheer--Doyen parameters provide upper bounds on the permutation ranks of the groups induced on the imprimitivity system and on a class of the system. We explore extreme cases where these bounds are attained, give a new construction for a family of designs achieving these bounds, and pose several open questions concerning the Delandtsheer--Doyen parameters.
Cite
@article{arxiv.2009.00282,
title = {Delandtsheer--Doyen parameters for block-transitive point-imprimitive 2-designs},
author = {Carmen Amarra and Alice Devillers and Cheryl E. Praeger},
journal= {arXiv preprint arXiv:2009.00282},
year = {2020}
}
Comments
12 pages. The research in this paper forms part of Australian Research Council Discovery Project DP200100080. It is also an outcome of the February 2019 Research Retreat of the Centre for the Mathematics of Symmetry and Computation, at the University of Western Australia