Short proofs for cut-and-paste sorting of permutations

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 2n/3 such moves and that some permutations require at least n/2 moves.

• Type: Journal
• Year: 2007
• Where: DM
• Authors: Daniel W. Cranston, Ivan Hal Sudborough, Douglas B. West
• Keywords: Cut-and-paste Operations, DM 2007, Maximum Number, Permutations