Geoffrey Martin

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It has been conjectured that any partial triple system of order u and index λ can be embedded in a triple system of order v and index λ whenever v ≥ 2u + 1, λ(v − 1) is even and λ v 2 ≡ 0 (mod 3). This conjecture is known to hold for λ = 1 and for all even λ ≥ 2. Here the conjecture is proven for all remaining values of λ when u ≥ 28.
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