• Corpus ID: 222379688

Limits of Latin squares.

@article{Garbe2020LimitsOL,
  title={Limits of Latin squares.},
  author={Frederik Garbe and Robert Hancock and Jan Hladk'y and Maryam Sharifzadeh},
  journal={arXiv: Combinatorics},
  year={2020}
}

• Frederik Garbe, Robert Hancock, +1 author M. Sharifzadeh
• Published 15 October 2020
• Mathematics
• arXiv: Combinatorics

We develop a limit theory of Latin squares, paralleling the recent limit theories of dense graphs and permutations. We introduce a notion of density, an appropriate version of the cut distance, and a space of limit objects - so-called Latinons. Key results of our theory are the compactness of the limit space and the equivalence of the topologies induced by the cut distance and the left-convergence. Last, using Keevash's recent results on combinatorial designs, we prove that each Latinon can be approximated by a finite Latin square.