Toufik Mansour and Augustine O. Munagi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 1, Pages 81—91
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We enumerate partitions of the set according to occurrences of isolated successions, that is, integer strings in a block when neither nor 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.
- Isolated succession
- Generating function
2020 Mathematics Subject Classification
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- Mansour, T. (2013). Combinatorics of Set Partitions. CRC, Taylor & Francis Group, Boca Raton.
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- Received: 24 March 2021
- Revised: 14 February 2021
- Accepted: 15 February 2022
- Online First: 15 February 2022
Cite this paper
Mansour, T., & Munagi, A. O. (2022). Set partitions with isolated successions. Notes on Number Theory and Discrete Mathematics, 28(1), 81-91, DOI: 10.7546/nntdm.2022.28.1.81-91.