steiner triple system in design theory

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timer Asked: Dec 10th, 2017
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the problem about steiner triple system in design theory

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Borys S
School: UT Austin

I did it before bidding:)

We have π‘Ÿ red points, 𝑏 blue points and some quantity of triples, each of them containing
2π‘Ÿ + 𝑏 or 2𝑏 + π‘Ÿ. Also we know that each two distinct point are contained in exactly one
triple.
(a) how many triples of the 2π‘Ÿ + 𝑏 type? For each pair of distinct π‘Ÿ points there is only one
π‘Ÿ
π‘Ÿ(π‘Ÿβˆ’1)
triple containing them. The quantity of these pairs is ( ) = 2 .
2
𝑏(π‘βˆ’1)
𝑏
(b) the same way the quantity of 2𝑏 + π‘Ÿ triples is ( ) = 2 , i.e. there are
2
𝑏(𝑏 βˆ’ 1) + π‘Ÿ(π‘Ÿ βˆ’ 1)
2
triples at all.

From the other hand, each two points among all π‘Ÿ + 𝑏 have exactly one triple. This way...

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