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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