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Drizen, A.L.; Grannell, Mike and Griggs, Terry
(2011).
DOI: https://doi.org/10.1016/j.disc.2011.06.023
Abstract
A Steiner triple system of order , STS(
), may be called
to another STS(
) if one can be converted to the other by a sequence of three simple operations involving Pasch trades with a single negative block. It is conjectured that any two STS(
)s on the same base set are equivalent in this sense. We prove that the equivalence class containing a given system
on a base set
contains all the systems that can be obtained from
by any sequence of well over one hundred distinct trades, and that this equivalence class contains all isomorphic copies of
on
. We also show that there are trades which cannot be effected by means of Pasch trades with a single negative block.