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Short Proofs for Cut-and-Paste Sorting of Permutations

Daniel Cranston·I. Hal Sudborough·Douglas B. West
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Abstract

We consider the problem of determining the maximum number of moves required to sort a permutation of $[n]$ using cut-and-paste operations, in which a segment is cut out and then pasted into the remaining string, possibly reversed. We give short proofs that every permutation of $[n]$ can be transformed to the identity in at most $\flr{2n/3}$ such moves and that some permutations require at least $\flr{n/2}$ moves.

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Daniel Cranston, I. Hal Sudborough, Douglas B. West. 2006-05-03. Short Proofs for Cut-and-Paste Sorting of Permutations. https://arxiv.org/abs/math/0605084

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