Publication date: 31 December 2021
Volume: Vol 56
Issue: Svezak 2
Pages: 225-240
DOI: https://doi.org/10.3336/gm.56.2.02
Glasnik matematički, Vol. 56 No. 2, 2021.
Original scientific paper
https://doi.org/10.3336/gm.56.2.02
Groups \(S_{n}\times S_{m}\) in construction of flag-transitive block designs
Snježana Braić
; Faculty of science, University of Split, 21 000 Split, Croatia
Joško Mandić
; Faculty of science, University of Split, 21 000 Split, Croatia
Aljoša Šubašić
orcid.org/0000-0002-6943-0856
; Faculty of science, University of Split, 21 000 Split, Croatia
Tanja Vojković
orcid.org/0000-0002-8160-7757
; Faculty of science, University of Split, 21 000 Split, Croatia
Tanja Vučičić
; Faculty of science, University of Split, 21 000 Split, Croatia
Abstract
In this paper, we observe the possibility that the group \(S_{n}\times S_{m}\) acts
as a flag-transitive automorphism group of a block design with point set \(\{1,\ldots ,n\}\times \{1,\ldots ,m\},4\leq n\leq m\leq 70\). We prove the
equivalence of that problem to the existence of an appropriately defined
smaller flag-transitive incidence structure. By developing and applying
several algorithms for the construction of the latter structure, we manage
to solve the existence problem for the desired designs with \(nm\) points in
the given range. In the vast majority of the cases with confirmed existence,
we obtain all possible structures up to isomorphism.
Keywords
Combinatorial designs, incidence structures, automorphism groups
Hrčak ID:
267559
URI
Publication date:
23.12.2021.
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