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Reconstructing permutations from cycle minors
 Electr. J. Comb
"... Abstract The ith cycle minor of a permutation p of the set {1, 2, . . . , n} is the permutation formed by deleting an entry i from the decomposition of p into disjoint cycles and reducing each remaining entry larger than i by 1. In this paper, we show that any permutation of {1, 2, . . . , n} can b ..."
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Abstract The ith cycle minor of a permutation p of the set {1, 2, . . . , n} is the permutation formed by deleting an entry i from the decomposition of p into disjoint cycles and reducing each remaining entry larger than i by 1. In this paper, we show that any permutation of {1, 2, . . . , n} can be reconstructed from its set of cycle minors if and only if n ≥ 6. We then use this to provide an alternate proof of a known result on a related reconstruction problem.
Permutation Reconstruction from Differences
"... We prove that the problem of reconstructing a permutation pi1,..., pin of the integers [1... n] given the absolute differences pii+1 − pii, i = 1,..., n − 1 is NP– complete. As an intermediate step we first prove the NP–completeness of the decision version of a new puzzle game that we call Crazy ..."
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We prove that the problem of reconstructing a permutation pi1,..., pin of the integers [1... n] given the absolute differences pii+1 − pii, i = 1,..., n − 1 is NP– complete. As an intermediate step we first prove the NP–completeness of the decision version of a new puzzle game that we call Crazy Frog Puzzle. The permutation reconstruction from differences is one of the simplest combinatorial problems that have been proved to be computationally intractable. 1