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A set of triplets from {1,2,...,n}

Source: Kürschák 1988, problem 2

July 20, 2014
combinatorics unsolvedcombinatorics

Problem Statement

Set T⊂{1,2,…,n}3T\subset\{1,2,\dots,n\}^3 has the property that for any two triplets (a,b,c)(a,b,c) and (x,y,z)(x,y,z) in TT, we have a<b<ca<b<c, and also, we know that at most one of the equalities a=xa=x, b=yb=y, c=zc=z holds. Maximize ∣T∣|T|.
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