MathDB
Maximum number of subsets

Source: Miklós Schweitzer 2010 ,P3

September 9, 2020
college contestsMiklos Schweitzercombinatoricsset theorySubsets

Problem Statement

Let Ai,i=1,2,…,t A_i,i=1,2,\dots,t be distinct subsets of the base set {1,2,…,n}\{1,2,\dots,n\} complying to the following condition Ai∩Ak⊆Aj \displaystyle A_ {i} \cap A_ {k} \subseteq A_ {j}for any 1≤i<j<k≤t.1 \leq i <j <k \leq t. Find the maximum value of t.t. Thanks @dgrozev
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