On the number of distinct block sizes in partitions of a set

A. M. Odlyzko; L. B. Richmond

doi:10.1016/0097-3165(85)90066-4

On the number of distinct block sizes in partitions of a set

A. M. Odlyzko, L. B. Richmond

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

The average number of distinct block sizes in a partition of a set of n elements is asymptotic to e log n as n → ∞. In addition, almost all partitions have approximately e log n distinct block sizes. This is in striking contrast to the fact that the average total number of blocks in a partition is ∼n(log n)^-1 as n → ∞.

Original language	English (US)
Pages (from-to)	170-181
Number of pages	12
Journal	Journal of Combinatorial Theory, Series A
Volume	38
Issue number	2
DOIs	https://doi.org/10.1016/0097-3165(85)90066-4
State	Published - Mar 1985
Externally published	Yes

Publisher link

10.1016/0097-3165(85)90066-4

Find It

Find It at U of M Libraries

Cite this

@article{8956c79b7389419cb0fe8f8b9ed303d8,

title = "On the number of distinct block sizes in partitions of a set",

abstract = "The average number of distinct block sizes in a partition of a set of n elements is asymptotic to e log n as n → ∞. In addition, almost all partitions have approximately e log n distinct block sizes. This is in striking contrast to the fact that the average total number of blocks in a partition is ∼n(log n)-1 as n → ∞.",

author = "Odlyzko, {A. M.} and Richmond, {L. B.}",

year = "1985",

month = mar,

doi = "10.1016/0097-3165(85)90066-4",

language = "English (US)",

volume = "38",

pages = "170--181",

journal = "Journal of Combinatorial Theory, Series A",

issn = "0097-3165",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - On the number of distinct block sizes in partitions of a set

AU - Odlyzko, A. M.

AU - Richmond, L. B.

PY - 1985/3

Y1 - 1985/3

N2 - The average number of distinct block sizes in a partition of a set of n elements is asymptotic to e log n as n → ∞. In addition, almost all partitions have approximately e log n distinct block sizes. This is in striking contrast to the fact that the average total number of blocks in a partition is ∼n(log n)-1 as n → ∞.

AB - The average number of distinct block sizes in a partition of a set of n elements is asymptotic to e log n as n → ∞. In addition, almost all partitions have approximately e log n distinct block sizes. This is in striking contrast to the fact that the average total number of blocks in a partition is ∼n(log n)-1 as n → ∞.

UR - http://www.scopus.com/inward/record.url?scp=0010815872&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010815872&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(85)90066-4

DO - 10.1016/0097-3165(85)90066-4

M3 - Article

AN - SCOPUS:0010815872

SN - 0097-3165

VL - 38

SP - 170

EP - 181

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

IS - 2

ER -

On the number of distinct block sizes in partitions of a set

Abstract

Publisher link

Find It

Other files and links

Fingerprint

Cite this