In [2], the number of permutations of n objects with largest cycle length equal to k is studied in detail. The purpose of [3] which is summarized here is to show that these results generalize in a straightforward manner to all labelled sets, unlabelled sets and unlabelled powersets.
C(z)= 

c_{n}z^{n} or  C(z)= 

c_{n} 

, 
L(z) 


P(z) 


S(z) 

L 

(z)=exp 
æ ç ç è 


ö ÷ ÷ ø 
(e 

1)=(e 

1)L(z)exp 
æ ç ç è 
 


ö ÷ ÷ ø 
. (1) 


n/2<k£ n  

n/3<k£ n/2, 
L_{k}^{s}(z)=exp 
æ ç ç è 


ö ÷ ÷ ø 
(e 

1). 
[z^{n}]L_{k}^{s}(z) 

k=n,  
=0,  n/2<k<n,  

k=n/2,  

n/3<k<n/2,... 
This document was translated from L^{A}T_{E}X by H^{E}V^{E}A.