… Our method works for all latin squares satisfying a certain quasirandomness condition, …
random latin squares with high probability as well as multiplication tables of quasirandom groups. …

… A Latin square of order n is an urn:x-wiley:rsa:media:rsa21060:rsa21060-math-0011
matrix such that each row and each column contains each of the numbers urn:x-wiley:rsa:media:rsa21060:rsa21060-math-0012 …

… Next, we need the fact that the triangle removal process produces every quasirandom
partial Latin square with a comparable probability. This follows from the fact that quasirandom …

… ε,h m be the set of partial Latin squares P ∈ Lm such that G(P) is (ε, h)-quasirandom, and
let O ε,h m ⊆ Om be the set of ordered partial Latin squares L ∈ Om such that Li ∈ L ε,h …

… Latin square P, when can we complete P to a Latin square L? In this paper, we investigate
the class of ϵ-dense partial Latin squares: partial Latin squares in … results on Latin squares to …

… The desired property that almost all G ∈ Φ ( K n ↔ ) $$ G\in \Phi \left(\overleftrightarrow{K_n}\right)
$$ are lower-quasirandom will follow immediately from 26 (see Theorem 4.7 of the …

… A different property that likely holds aas for random Latin squares is that they have “low
discrepancy” or are “quasirandom” in a certain sense. This is related to a conjecture by Linial and …

… quasirandom if the induced density of every permutation σ in πn converges to 1/|σ|! as n →
∞. We prove that π1,π2,... is quasirandom if … latin square of order four induces a quasirandom-…

… Indeed, very shortly after we published this preprint at arXiv, Cooper, Král’, Lamaison, Mohr
[20] used our theory to characterise sequences of quasirandom Latin squares; see Section …

… Basically, we need a fractional triangledecomposition result for quasirandom tripartite
graphs. Suitable techniques in the dense tripartite setting have already been developed by …