In
combinatorics, a
Steiner Triple System of
order v is a
collection of
triples or 3-
subsets of a
set X of
size v such that each
pair of
elements of X occurs in exactly one
triple. In other words a
Steiner Triple System is a 2-
design with
parameters (v, 3, 1, (v-1)/2, v(v-1)/6) . Since the
design parameters must be
integers, it is necessary that v = 6n + 1 or v = 6n + 3.
Kirkman showed that this is a
sufficient condition that a
Steiner Triple System exists (see
Reverend Kirkman's Schoolgirls).
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