The number of distinct part sizes in a random integer partition
โ Scribed by William M.Y Goh; Eric Schmutz
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 290 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0097-3165
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๐ SIMILAR VOLUMES
Let Q(n) denote the number of partitions of an integer n into distinct parts. For positive integers j, the first author and B. Gordon proved that Q(n) is a multiple of 2 j for every non-negative integer n outside a set with density zero. Here we show that if i 0 (mod 2 j ), then In particular, Q(n)
Central and local limit theorems are derived for the number of distinct summands in integer partitions, with or without repetitions, under a general scheme essentially due to Meinardus. The local limit theorems are of the form of Crame rtype large deviations and are proved by Mellin transform and th
Let be a partition of an integer n chosen uniformly at random among all ลฝ . such partitions. Let s be a part size chosen uniformly at random from the set of all part ลฝ . sizes that occur in . We prove that, for every fixed m G 1, the probability that s has ลฝ ลฝ .. multiplicity m in approaches 1r m mq
We investigate from probabilistic point of view the asymptotic behavior of the number of distinct component sizes in general classes of combinatorial structures of size n as n ร . Mild restrictions of admissibility type are imposed on the corresponding generating functions and asymptotic expressions