Where the Typical Set Partitions Meet and Join

The lattice of the set partitions of [n] ordered by refinement is studied. Suppose r partitions p1, . . . , pr are chosen independently and uniformly at random. The probability that the coarsest refinement of all pi 's is the finest partition {1}, . . . , {n} is shown to approach 0 for r = 2, and 1 for r 3. The probability that the finest coarsening of all pi 's is the one-block partition is shown to approach 1 for every r 2.

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Boris Pittel
• Keywords: Coarsest Refinement, COMBINATORICS 2000, Finest Partition, Set Partitions