Combinatorics MOC

Steiner system

An S⁡(𝑡,𝑘,𝑛) Steiner system is a set Ω of 𝑛 points, together with a set of 𝑘-element subsets 𝐵 ⊆P(Ω), called blocks or 𝑘-ads, such that any set of 𝑡 points is contained in exactly one 𝑘-ad. comb Excluding trivial systems, 1 <𝑡 <𝑘 <𝑛.

• A finite projective plane of order 𝑞 is an S⁡(2,𝑞 +1,𝑞2 +𝑞 +1). In particular the Fano plane is the unique [[Fano plane|S⁡(2,3,7)]] Steiner system.

Special Steiner systems

• [[Fano plane|S⁡(2,3,7)]]
• S(5,8,24)

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