Compositions of Random Functions on a Finite Set

If we compose sufficiently many random functions on a finite set, then the composite function will be constant. We determine the number of compositions that are needed, on average. Choose random functions f1, f2, f3, . . . independently and uniformly from among the nn functions from [n] into [n]. For t > 1, let gt = ft ft-1

• Type: Journal
• Year: 2002
• Where: COMBINATORICS
• Authors: Avinash Dalal, Eric Schmutz
• Keywords: COMBINATORICS 2002, Composite Function, Expected Value, Random Functions