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PreprintCC BY 4.0arXiv

Maximum length and size of simultaneous core partitions with distinct parts

  • Metin Can Aydemir
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Abstract

We give, for the first time, a formula for the largest size of an (s,t)-core partition with distinct parts valid for every coprime pair. We also determine the greatest number of parts of an (s,t)-core partition whose successive parts differ by at least D, whenever gcd(s,t)≤ D, removing the restrictions on the core parameters in the formula of Burson, Sisneros-Thiry, and Straub. The size formula uses a column description and a single Dedekind sum. The length formula uses coefficients from the Euclidean algorithm and satisfies a recurrence in smaller core parameters. We construct partitions attaining each maximum.

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Cite

BibTeXRIS
BibTeX
@misc{aydemir2026maximum,
  title = {{Maximum length and size of simultaneous core partitions with distinct parts}},
  author = {Metin Can Aydemir},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35322},
  eprint = {2610.35322},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35322},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Maximum length and size of simultaneous core partitions with distinct parts
AU  - Metin Can Aydemir
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35322
UR  - https://arxiv.org/abs/2610.35322
AB  - We give, for the first time, a formula for the largest size of an (s,t)-core partition with distinct parts valid for every coprime pair. We also determine the greatest number of parts of an (s,t)-core partition whose successive parts differ by at least D, whenever gcd(s,t)≤ D, removing the restrictions on the core parameters in the formula of Burson, Sisneros-Thiry, and Straub. The size formula uses a column description and a single Dedekind sum. The length formula uses coefficients from the Euclidean algorithm and satisfies a recurrence in smaller core parameters. We construct partitions attaining each maximum.
ER  -