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On the number of \(k\)-compositions \(n\) satisfying certain coprimality conditions

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Abstract

We generalize the asymptotic estimates by Bubboloni, Luca and Spiga [2] on the number of \(k\)-compositions of n satisfying some coprimality conditions. We substantially refine the error term concerning the number of \(k\)-compositions of \(n\) with pairwise relatively prime summands. We use a different approach, based on properties of multiplicative arithmetic functions of \(k\) variables and on an asymptotic formula for the restricted partition function.

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Acknowledgement

The author thanks the referee for useful comments and suggestions concerning the presentation of the proofs of the paper.

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  1. Department of Mathematics, University of Pécs, Ifjúság útja 6, 7624, Pécs, Hungary

    L. Tóth

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  1. L. Tóth
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Correspondence to L. Tóth.

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The research was financed by NKFIH in Hungary, within the framework of the 2020-4.1.1- TKP2020 3rd thematic programme of the University of Pécs.

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Tóth, L. On the number of \(k\)-compositions \(n\) satisfying certain coprimality conditions. Acta Math. Hungar. 164, 135–156 (2021). https://doi.org/10.1007/s10474-021-01147-5

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  • DOI: https://doi.org/10.1007/s10474-021-01147-5

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