Name
Abstract | ||
|---|---|---|
Let lambda be a partition of an integer n chosen uniformly at random among all such partitions. Let s(lambda) be a part size chosen uniformly at random from the set of all part sizes that occur in lambda. We prove that, for every fixed m greater than or equal to 1, the probability that s(lambda) has multiplicity m in A approaches 1/(m(m + 1)) as n ---> infinity. Thus, for example, the limiting probability that a random part size in a random partition is unrepeated is 1/2. In addition, (a) for the average number of different part sizes, we refine an asymptotic estimate given by Wilf, (b) we derive an asymptotic estimate of the average number of parts of given multiplicity m, and (c) we show that the expected multiplicity of a randomly chosen part size of a random partition of n is asymptotic to (log n)/2. The proofs of the main result and of (c) use a conditioning device of Fristedt. (C) 1999 John Wiley & Sons, Inc. |
Year | DOI | Venue |
|---|---|---|
1999 | 3.0.CO;2-F" target="_self" class="small-link-text"10.1002/(SICI)1098-2418(199903)14:23.0.CO;2-F | Random Struct. Algorithms |
Field | DocType | Volume |
Integer,Discrete mathematics,Combinatorics,struct,Multiplicity (mathematics),Mathematical proof,Partition (number theory),Mathematics,Limiting | Journal | 14 |
Issue | ISSN | Citations |
2 | 1042-9832 | 18 |
PageRank | References | Authors |
2.15 | 2 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sylvie Corteel | 1 | 266 | 36.33 |
| BORIS PITTEL | 2 | 621 | 135.03 |
| Carla D. Savage | 3 | 349 | 60.16 |
| Herbert S. Wilf | 4 | 498 | 172.87 |