Set partitions with circular successions

Toufik Mansour; Augustine O. Munagi

doi:10.1016/j.ejc.2014.06.008

Set partitions with circular successions

Toufik Mansour, Augustine O. Munagi

Department of Mathematics

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

Abstract

We consider the enumeration of partitions of a finite set according to the number of consecutive elements inside a block under the assumption that the elements are arranged around a circle. This statistic, commonly known as circular succession, continues to play a significant role in many combinatorial problems involving combinations of a set following its first appearance in a paper of Irving Kaplansky in the 1940s. In this paper we obtain interesting formulas for the number of partitions avoiding a circular succession and the number of partitions containing a specified number of circular successions. Our methods include both elementary combinatorial reasoning and the application of ordinary and exponential power series generating functions. Several new combinatorial identities are also stated.

Original language	English
Pages (from-to)	207-216
Number of pages	10
Journal	European Journal of Combinatorics
Volume	42
DOIs	https://doi.org/10.1016/j.ejc.2014.06.008
State	Published - Nov 2014

Bibliographical note

Funding Information:
The authors are grateful to the anonymous referees for constructive comments which led to improvements in exposition. The second author was partially supported by the National Research Foundation of South Africa under grant number 80860 .

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.ejc.2014.06.008

Cite this

@article{09c0101f504546cfbfc446d459222cc4,

title = "Set partitions with circular successions",

abstract = "We consider the enumeration of partitions of a finite set according to the number of consecutive elements inside a block under the assumption that the elements are arranged around a circle. This statistic, commonly known as circular succession, continues to play a significant role in many combinatorial problems involving combinations of a set following its first appearance in a paper of Irving Kaplansky in the 1940s. In this paper we obtain interesting formulas for the number of partitions avoiding a circular succession and the number of partitions containing a specified number of circular successions. Our methods include both elementary combinatorial reasoning and the application of ordinary and exponential power series generating functions. Several new combinatorial identities are also stated.",

author = "Toufik Mansour and Munagi, {Augustine O.}",

note = "Funding Information: The authors are grateful to the anonymous referees for constructive comments which led to improvements in exposition. The second author was partially supported by the National Research Foundation of South Africa under grant number 80860 . ",

year = "2014",

month = nov,

doi = "10.1016/j.ejc.2014.06.008",

language = "English",

volume = "42",

pages = "207--216",

journal = "European Journal of Combinatorics",

issn = "0195-6698",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Set partitions with circular successions

AU - Mansour, Toufik

AU - Munagi, Augustine O.

N1 - Funding Information: The authors are grateful to the anonymous referees for constructive comments which led to improvements in exposition. The second author was partially supported by the National Research Foundation of South Africa under grant number 80860 .

PY - 2014/11

Y1 - 2014/11

N2 - We consider the enumeration of partitions of a finite set according to the number of consecutive elements inside a block under the assumption that the elements are arranged around a circle. This statistic, commonly known as circular succession, continues to play a significant role in many combinatorial problems involving combinations of a set following its first appearance in a paper of Irving Kaplansky in the 1940s. In this paper we obtain interesting formulas for the number of partitions avoiding a circular succession and the number of partitions containing a specified number of circular successions. Our methods include both elementary combinatorial reasoning and the application of ordinary and exponential power series generating functions. Several new combinatorial identities are also stated.

AB - We consider the enumeration of partitions of a finite set according to the number of consecutive elements inside a block under the assumption that the elements are arranged around a circle. This statistic, commonly known as circular succession, continues to play a significant role in many combinatorial problems involving combinations of a set following its first appearance in a paper of Irving Kaplansky in the 1940s. In this paper we obtain interesting formulas for the number of partitions avoiding a circular succession and the number of partitions containing a specified number of circular successions. Our methods include both elementary combinatorial reasoning and the application of ordinary and exponential power series generating functions. Several new combinatorial identities are also stated.

UR - http://www.scopus.com/inward/record.url?scp=84904515975&partnerID=8YFLogxK

U2 - 10.1016/j.ejc.2014.06.008

DO - 10.1016/j.ejc.2014.06.008

M3 - Article

AN - SCOPUS:84904515975

SN - 0195-6698

VL - 42

SP - 207

EP - 216

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

ER -

Set partitions with circular successions

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this