Sorting by Replacement Selecting
In sorting by replacement selecting, the expected
length of a sequence beginning with the i-th 
element (i>1) is proved to be 2F, in accordance with
a conjecture of E. H. Friend, where F is the number 
of memory cells used.  The expected length of the j-th
sequence is determined to be F times a j-th degree 
polynomial in e, such that the value of this polynomial
approaches 2 as j approaches infinity.  Recursive 
formulas are obtained for both the mean and the standard
deviation of the length of the j-th sequence. 
 The mathematical proofs of these results are based
upon the assumption that n, the number of items to 
be sorted, is infinite, but it is shown that the error
due to the finiteness of n approaches zero rapidly 
as n increases.
CACM February, 1967
Gasner, B. J.
