The least k such that every permutation of length n is determined by its multiset of k-subsequence patterns is between exp(Omega(sqrt(ln n))) and O(sqrt(n ln n)).
Unique reconstruction of c oded strings from multiset substring spectra,
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Improvements on Permutation Reconstruction from Minors
The least k such that every permutation of length n is determined by its multiset of k-subsequence patterns is between exp(Omega(sqrt(ln n))) and O(sqrt(n ln n)).