Journal article
The number of distinct part sizes in a random integer partition
Journal of combinatorial theory. Series A, v 69(1), pp 149-158
1995
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Abstract
We prove a central limit theorem for the number of different part sizes in a random integer partition. If λ is one of the
P(
n) partitions of the integer
n, let D
n
(λ) be the number of distinct part sizes that λ has. (Each part size counts once, even though there may be many parts of a given size.) For any fixed
x,
#(λ:
D
n(λ) ⩽ A
n + xB
n}
P(n)
→
1
2π
∫
−∞
x
ℓ
−t
2
2
dt
as
n → ∞, where
A
n = (√6/π)n
1
2
and
B
n = (ρ6/2π − √54/π
3)
1
2
n
1
4
.
Metrics
Details
- Title
- The number of distinct part sizes in a random integer partition
- Creators
- William M.Y Goh - Drexel UniversityEric Schmutz - Drexel University
- Publication Details
- Journal of combinatorial theory. Series A, v 69(1), pp 149-158
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- [Retired Faculty]; Mathematics
- Web of Science ID
- WOS:A1995QA08400009
- Scopus ID
- 2-s2.0-0001568776
- Other Identifier
- 991019173974704721
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- Web of Science research areas
- Mathematics