Asymptotic normality and combinatorial aspects of the prefix exchange distance distribution
Combinatorics
2022-08-29 v1
Abstract
The prefix exchange distance of a permutation is the minimum number of exchanges involving the leftmost element that sorts the permutation. We give new combinatorial proofs of known results on the distribution of the prefix exchange distance for a random uniform permutation. We also obtain expressions for the mean and the variance of this distribution, and finally, we show that the normalised prefix exchange distribution converges in distribution to the standard normal distribution.
Keywords
Cite
@article{arxiv.1604.04766,
title = {Asymptotic normality and combinatorial aspects of the prefix exchange distance distribution},
author = {Simona Grusea and Anthony Labarre},
journal= {arXiv preprint arXiv:1604.04766},
year = {2022}
}
Comments
To appear in Advances in Applied Mathematics