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Concave and convex compositions

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Abstract

In a previous work, concave compositions were defined with the restriction that there be essentially the same number of parts on each side of the minimal part. In this work, we drop that restriction, and, in addition, we consider convex compositions as well. We shall link the related generating functions to combinations of classical, false, or mock theta functions and other Appell–Lerch sums.

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    George E. Andrews

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  1. George E. Andrews
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Correspondence to George E. Andrews.

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Dedicated to my good friends, Mourad Ismail and Dennis Stanton

Partially supported by National Science Foundation Grant DMS-0801184.

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Andrews, G.E. Concave and convex compositions. Ramanujan J 31, 67–82 (2013). https://doi.org/10.1007/s11139-012-9394-6

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  • DOI: https://doi.org/10.1007/s11139-012-9394-6

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