PreprintCC BY 4.0arXiv
Avoiding a partial Latin square with an isotope of a given Latin square
Abstract
For all sufficiently large n, we prove that every Latin square of order n can be made to avoid any prescribed partial Latin square of order n by permuting only its rows and columns. The proof combines Hall's theorem with elementary estimates for a random permutation.
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BibTeX
@misc{cambie2026avoiding,
title = {{Avoiding a partial Latin square with an isotope of a given Latin square}},
author = {Stijn Cambie and Ian M. Wanless},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20008},
eprint = {2610.20008},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20008},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Avoiding a partial Latin square with an isotope of a given Latin square
AU - Stijn Cambie
AU - Ian M. Wanless
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20008
UR - https://arxiv.org/abs/2610.20008
AB - For all sufficiently large n, we prove that every Latin square of order n can be made to avoid any prescribed partial Latin square of order n by permuting only its rows and columns. The proof combines Hall's theorem with elementary estimates for a random permutation.
ER -