Representing Permutations with Few Moves

@article{Bereg2016RepresentingPW,
  title={Representing Permutations with Few Moves},
  author={Sergey Bereg and Alexander E. Holroyd and Lev Nachmanson and Sergey Pupyrev},
  journal={SIAM J. Discret. Math.},
  year={2016},
  volume={30},
  pages={1950-1977}
}
Consider a finite sequence of permutations of the elements 1,...,n, with the property that each element changes its position by at most 1 from any permutation to the next. We call such a sequence a tangle, and we define a move of element i to be a maximal subsequence of at least two consecutive permutations during which its positions form an arithmetic progression of common difference +1 or -1. We prove that for any initial and final permutations, there is a tangle connecting them in which each… 
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