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An Upper Bound on the Number of Circular Transpositions to Sort a
Permutation
release_y352bmohnbfvxl6mjhpy5dmdpe
by
Anke van Zuylen, James Bieron, Frans Schalekamp, Gexin Yu
Released
as a article
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2014
Abstract
We consider the problem of upper bounding the number of circular
transpositions needed to sort a permutation. It is well known that any
permutation can be sorted using at most n(n-1)/2 adjacent transpositions. We
show that, if we allow all adjacent transpositions, as well as the
transposition that interchanges the element in position 1 with the element in
the last position, then the number of transpositions needed is at most n^2/4.
This answers an open question posed by Feng, Chitturi and Sudborough (2010).
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1402.4867v1
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