OF PERMUTATIONS INTO n-CYCLES*
Richard P. STANLEk · 1981
Using the character theory of the symmetric group ES,,, an explicit formula is derived for the number Q(V) of ways of writing a permutation TT E S;,, as a product of k n-cycles. From this the asymptotic expansion for gk(n) is derived, provided that when i. = 2, T has O(log n) fixed points. In particular, there follows a conjecture of Walkup that if 71;, EG,, is an even permutation with no fixed point ., then lim,,, gJn,,)/(n -2)! = 2.