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On the integer partitions recursive structure

Number Theory 2026-03-09 v1

Abstract

Sylvester showed that the partition of an integer into a set of positive integers can be represented as a sum of the polynomial term and quasiperiodic components called the Sylvester waves. The wave itself is a weighted sum of the polynomial terms multiplied by the periodic functions. The integer weights are found to be a sum of partitions into a smaller set of integers implying the recursive structure of integer partitions.

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Cite

@article{arxiv.2603.06438,
  title  = {On the integer partitions recursive structure},
  author = {Boris Y. Rubinstein},
  journal= {arXiv preprint arXiv:2603.06438},
  year   = {2026}
}

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4 pages