๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The number of distinct part sizes in a random integer partition

โœ 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

No coin nor oath required. For personal study only.


๐Ÿ“œ SIMILAR VOLUMES


The 2-Adic Behavior of the Number of Par
โœ Ken Ono; David Penniston ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 171 KB

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)

Limit Theorems for the Number of Summand
โœ Hsien-Kuei Hwang ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 254 KB

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

On the multiplicity of parts in a random
โœ Sylvie Corteel; Boris Pittel; Carla D. Savage; Herbert S. Wilf ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 200 KB ๐Ÿ‘ 2 views

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

Limiting Distributions for the Number of
โœ Ljuben Mutafchiev ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 428 KB

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