Note on random Latin squares and the triangle removal process

Matthew Kwan; Ashwin Sah; Mehtaab Sawhney

Note on random Latin squares and the triangle removal process

Combinatorics 2021-10-01 v1

Authors: Matthew Kwan , Ashwin Sah , Mehtaab Sawhney

Abstract

This is a companion note to the paper "Almost all Steiner triple systems have perfect matchings (arXiv:1611.02246). That paper contains several general lemmas about random Steiner triple systems; in this note we record analogues of these lemmas for random Latin squares, which in particular are necessary ingredients for our recent paper "Large deviations in random Latin squares" (arXiv:2106.11932). Most important is a relationship between uniformly random order- $n$ Latin squares and the triangle removal process on the complete tripartite graph $K_{n,n,n}$ .

Cite

@article{arxiv.2109.15201,
  title  = {Note on random Latin squares and the triangle removal process},
  author = {Matthew Kwan and Ashwin Sah and Mehtaab Sawhney},
  journal= {arXiv preprint arXiv:2109.15201},
  year   = {2021}
}

Comments

arXiv admin note: text overlap with arXiv:1611.02246

Note on random Latin squares and the triangle removal process

Abstract

Cite

Comments

Related papers