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k-element subsets with strict relation

Source: Kürschák 2016, problem 1

October 7, 2016
combinatoricsSubsets

Problem Statement

Let 1≤k≤n1\le k\le n be integers. At most how many kk-element subsets can we select from {1,2,…,n}\{1,2,\dots,n\} such that for any two selected subsets, one of the subsets consists of the kk smallest elements of their union?
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