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PreprintCC BY 4.0arXiv

Counting and constructing Latin tableaux

  • Spencer Daugherty
  • Michaela Fahnesock
  • Shawn Huxtable
  • Michael Larson
  • Nourah Al Munayes
  • Storey Peacock
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Abstract

Latin tableaux generalize Latin squares to Young diagrams and have interesting connections to linear algebra and Rota's basis conjecture. Conjecturally, a partition admits Latin tableaux if and only if it belongs to a special class called wide partitions. We prove that various classes of wide partitions admit Latin tableaux. We extend these classes further by showing that the number of Latin tableaux is weakly increasing over certain operations on wide partitions. Additionally, we establish an explicit formula for the number of Latin tableaux using (0,1)-matrices and matrix permanents.

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Cite

BibTeXRIS
BibTeX
@misc{daugherty2026counting,
  title = {{Counting and constructing Latin tableaux}},
  author = {Spencer Daugherty and Michaela Fahnesock and Shawn Huxtable and Michael Larson and Nourah Al Munayes and Storey Peacock},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29291},
  eprint = {2610.29291},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29291},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Counting and constructing Latin tableaux
AU  - Spencer Daugherty
AU  - Michaela Fahnesock
AU  - Shawn Huxtable
AU  - Michael Larson
AU  - Nourah Al Munayes
AU  - Storey Peacock
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29291
UR  - https://arxiv.org/abs/2610.29291
AB  - Latin tableaux generalize Latin squares to Young diagrams and have interesting connections to linear algebra and Rota's basis conjecture. Conjecturally, a partition admits Latin tableaux if and only if it belongs to a special class called wide partitions. We prove that various classes of wide partitions admit Latin tableaux. We extend these classes further by showing that the number of Latin tableaux is weakly increasing over certain operations on wide partitions. Additionally, we establish an explicit formula for the number of Latin tableaux using (0,1)-matrices and matrix permanents.
ER  -