A characterization of the set of fixed points of the Quicksort transformation
<|reference_start|>A characterization of the set of fixed points of the Quicksort transformation: The limiting distribution \mu of the normalized number of key comparisons required by the Quicksort sorting algorithm is known to be the unique fixed point of a certain distributional transformation T -- unique, that is, subject to the constraints of zero mean and finite variance. We show that a distribution is a fixed point of T if and only if it is the convolution of \mu with a Cauchy distribution of arbitrary center and scale. In particular, therefore, \mu is the unique fixed point of T having zero mean.<|reference_end|>
@article{fill2000a,
    title={A characterization of the set of fixed points of the Quicksort
  transformation},
    author={James Allen Fill (Johns Hopkins Univ.), Svante Janson (Uppsala Univ.)},
    journal={arXiv preprint arXiv:math/0005236},
    year={2000},
    number={606, Department of Mathematical Sciences, The Johns Hopkins
  University},
    archivePrefix={arXiv},
    eprint={math/0005236},
    primaryClass={math.PR cs.DS}
}