A. David Christopher
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 1, Pages 100—108
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Let and be two positive integers and let be a set of positive integers. We define to be the number of partitions of with exactly sizes and parts in . As an implication of a variant of Newton’s product-sum identities we present a generating function for . Subsequently, we obtain a recurrence relation for and a divisor-sum expression for . Also, we present a bijective proof for the latter expression.
- Newton’s product-sum identities
- Size of a partition
- Recurrence relation
2020 Mathematics Subject Classification
- Primary 05A17
- Secondary 11P99
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- Received: 19 October 2020
- Revised: 1 October 2021
- Accepted: 18 February 2022
- Online First: 19 February 2022
Cite this paper
David Christopher, A. (2022). Partitions with k sizes from a set. Notes on Number Theory and Discrete Mathematics, 28(1), 100-108, DOI: 10.7546/nntdm.2022.28.1.100-108.