Set partitions with isolated successions

T Mansour; AO Munagi

doi:10.7546/nntdm.2022.28.1.81-91

Set partitions with isolated successions

T Mansour, AO Munagi

Department of Mathematics

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

Abstract

We enumerate partitions of the set {1, ... , n} according to occurrences of isolated successions, that is, integer strings a, a + 1, ... , b in a block when neither a - 1 nor b + 1 lies in the same block. Our results include explicit formulas and generating functions for the number of partitions containing isolated successions of a given length. We also consider a corresponding analog of the associated Stirling numbers of the second kind.

Original language	English
Pages (from-to)	81-91
Number of pages	11
Journal	Notes on Number Theory and Discrete Mathematics
Volume	28
Issue number	1
DOIs	https://doi.org/10.7546/nntdm.2022.28.1.81-91
State	Published - 2022

Bibliographical note

Times Cited in Web of Science Core Collection: 1 Total Times Cited: 1 Cited Reference Count: 9

Keywords

Partition
Isolated succession
Recurrence
Generating function

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10.7546/nntdm.2022.28.1.81-91

http://nntdm.net/papers/nntdm-28/NNTDM-28-1-081-091.pdf

Cite this

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abstract = "We enumerate partitions of the set {1, ... , n} according to occurrences of isolated successions, that is, integer strings a, a + 1, ... , b in a block when neither a - 1 nor b + 1 lies in the same block. Our results include explicit formulas and generating functions for the number of partitions containing isolated successions of a given length. We also consider a corresponding analog of the associated Stirling numbers of the second kind.",

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AU - Munagi, AO

N1 - Times Cited in Web of Science Core Collection: 1 Total Times Cited: 1 Cited Reference Count: 9

PY - 2022

Y1 - 2022

N2 - We enumerate partitions of the set {1, ... , n} according to occurrences of isolated successions, that is, integer strings a, a + 1, ... , b in a block when neither a - 1 nor b + 1 lies in the same block. Our results include explicit formulas and generating functions for the number of partitions containing isolated successions of a given length. We also consider a corresponding analog of the associated Stirling numbers of the second kind.

AB - We enumerate partitions of the set {1, ... , n} according to occurrences of isolated successions, that is, integer strings a, a + 1, ... , b in a block when neither a - 1 nor b + 1 lies in the same block. Our results include explicit formulas and generating functions for the number of partitions containing isolated successions of a given length. We also consider a corresponding analog of the associated Stirling numbers of the second kind.

KW - Partition

KW - Isolated succession

KW - Recurrence

KW - Generating function

U2 - 10.7546/nntdm.2022.28.1.81-91

DO - 10.7546/nntdm.2022.28.1.81-91

M3 - Article

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VL - 28

SP - 81

EP - 91

JO - Notes on Number Theory and Discrete Mathematics

JF - Notes on Number Theory and Discrete Mathematics

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ER -

Set partitions with isolated successions

Abstract

Bibliographical note

Keywords

Access to Document

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Cite this