@booklet {gonczarowski-tdotclosciarp2013,
	title = {Distribution of the Combined Length of Spanned Cycles in a Random Permutation, The},
	howpublished = {Discussion Papers},
	year = {2013},
	month = {11},
	abstract = {For a random permutation on 1,2, {\textbrokenbar},n for fixed n, and for M{\v S}{\textdagger}1,2, {\textbrokenbar},n, we analyse the distribution of the combined length L=L(,M) of all cycles of that contain at least one element of M. We give a simple, explicit formula for the probability of every possible value for L (backed by three proofs of distinct flavours), as well as closed-form formulae for its expectation and variance, showing that less than 1/(|M|+1) of the elements 1, {\textbrokenbar},n are expected to be contained in cycles of that are disjoint from M, with low probability for a large deviation from this fraction. We furthermore give a simple explicit formula for all rising-factorial moments of L. These results are applicable to the study of manipulation in matching markets.},
	url = {/files/dp650.pdf},
	author = {Yannai A. Gonczarowski}
}
