Let S be a set of binary strings a1 ...an of length n (where juxtaposition means
Chapter 4, Problem 72(choose chapter or problem)
Let S be a set of binary strings a1 ...an of length n (where juxtaposition means concatenation). We call S k-complete if for any indices 1 i1 < < ik n and any binary string b1 ...bk of length k, there is a string s1 ...sn in S such that si1 si2 ...sik = b1b2 ...bk. For example, for n = 3, the set S = {001, 010, 011, 100, 101, 110} is 2-complete since all 4 patterns of 0s and 1s of length 2 can be found in any 2 positions. Show that if n k 2k(1 2k) m < 1, then there exists a k-complete set of size at most m.
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