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PreprintCC BY 4.0arXiv

River ribbon tableaux and symmetric group characters

  • Lucas Teyssier
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Abstract

We introduce river ribbon tableaux, where a river of non-trivial ribbons is placed between two banks of single boxes. Compared to other ribbon peelings, this reduces the geometric differences across diagrams of different shapes, and the maximal number of ribbon configurations. This allows us to prove a uniform character bound for symmetric groups which, specialized to balanced diagrams, proves the conjecture of Moore and Russell. As an application, we prove a conjecture of Dousse and Féray on the number of standard tableaux of skew shapes.

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Cite

BibTeXRIS
BibTeX
@misc{teyssier2026river,
  title = {{River ribbon tableaux and symmetric group characters}},
  author = {Lucas Teyssier},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18239},
  eprint = {2610.18239},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18239},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - River ribbon tableaux and symmetric group characters
AU  - Lucas Teyssier
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18239
UR  - https://arxiv.org/abs/2610.18239
AB  - We introduce river ribbon tableaux, where a river of non-trivial ribbons is placed between two banks of single boxes. Compared to other ribbon peelings, this reduces the geometric differences across diagrams of different shapes, and the maximal number of ribbon configurations. This allows us to prove a uniform character bound for symmetric groups which, specialized to balanced diagrams, proves the conjecture of Moore and Russell. As an application, we prove a conjecture of Dousse and Féray on the number of standard tableaux of skew shapes.
ER  -