A tight upper bound on the number of cyclically adjacent transpositions to sort a permutation

Zuylen, Anke van; Bieron, James C.; Schalekamp, Frans; Yu, Gexin

doi:10.1016/j.ipl.2016.06.006

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…In the case of sorting the permutation π(x) = x + ⌊N/2⌋, at least N 2 /4 swaps are required due to the distance of each number from its destination. This has recently been proved to be the worst case [vZBSY14]. By the above discussion, writhe considerations easily yield a very close bound of (N − 1) 2 /4 transpositions, for π(x) = N − x.…”

Section: Extreme Valuesmentioning

confidence: 62%

“…A related notion of weighted inversion numbers was considered by Kadell [20]. In Section 3 we discuss the relation of the writhe to other combinatorial notions, such as the alternating inversion number [6], and circular bubble sort [19,30]. We also fit the writhe into the context of nonparametric statistics for circular rank correlation [14,15].…”

Section: Introductionmentioning

confidence: 99%

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The writhe of permutations and random framed knots

Even-Zohar

2016

Random Struct. Alg.

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We introduce and study the writhe of a permutation, a circular variant of the well-known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled uniformly at random, we study the asymptotics of the writhe, and obtain a non-Gaussian limit distribution.This work is motivated by the study of random knots. A model for random framed knots is described, which refines the Petaluma model, studied in [EZHLN16]. The distribution of the framing in this model is equivalent to the writhe of random permutations.

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Section: Extreme Valuesmentioning

confidence: 62%

Section: Introductionmentioning

confidence: 99%

The writhe of permutations and random framed knots

Even-Zohar

2016

Random Struct. Alg.

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“…In[15], the corresponding claim is stated for a set of n positive integers instead of a permutation of[n]. Hence, the proof in[15] extends some notions on a permutation of [n] to a set of positive integers. On the other hand, our description here is straightforward and attains a short proof.…”

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confidence: 99%