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arXiv · 2004.09505

A complete solution of the partition of a number into arithmetic progressions

F. Javier de Vega
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Abstract

We solve the enumeration of the set $\textrm{AP}(n)$ of partitions of a positive integer $n$ in which the nondecreasing sequence of parts forms an arithmetic progression. In particular, we establish a formula for the number of nondecreasing arithmetic progressions of positive integers with sum $n$. We also present an explicit method to calculate all the partitions of $\textrm{AP}(n)$.

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F. Javier de Vega. 2020-04-20. A complete solution of the partition of a number into arithmetic progressions. https://doi.org/10.17654/0972555522006

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