Generalizing inplace multiplicity identities for integer compositions

Augustine O. Munagi, James A. Sellers

Research output: Contribution to journalArticlepeer-review


In a recent paper, the authors gave two new identities for compositions, or ordered partitions, of integers. These identities were based on closely-related integer partition functions which have recently been studied. In the process, we also extensively generalized both of these identities. Since then, we asked whether one could generalize one of these results even further by considering compositions in which certain parts could come from t kinds (rather than just two kinds, which was the crux of the original result). In this paper, we provide such a generalization. A straightforward bijective proof is given and generating functions are provided for each of the types of compositions which arise. We close by briefly mentioning some arithmetic properties satisfied by the functions which count such compositions.

Original languageEnglish (US)
Pages (from-to)41-48
Number of pages8
JournalQuaestiones Mathematicae
Issue number1
StatePublished - Sep 16 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 NISC (Pty) Ltd.


  • Composition
  • Generating function
  • Inplace
  • Partition


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