论文标题
quasirandom拉丁正方形的横向
Transversals in quasirandom latin squares
论文作者
论文摘要
$ n \ times n $ latin Square中的横向是$ n $条目的集合，不重复任何行，列或符号。关表明，几乎每$ n \ times n $ latin Square都有$ \ bigl（（1 + o（1））n / e^2 \ bigr）^n $ transersals to $ n \ to \ infty $。使用圆方法的松散变体，我们将其锐化为$（e^{ - 1/2} + o（1））n！^2 / n^n $。我们的方法适用于满足某种quasirandomness条件的所有拉丁平方，其中包括具有较高概率的随机拉丁正方形以及quasirandom组的乘法表。
A transversal in an $n \times n$ latin square is a collection of $n$ entries not repeating any row, column, or symbol. Kwan showed that almost every $n \times n$ latin square has $\bigl((1 + o(1)) n / e^2\bigr)^n$ transversals as $n \to \infty$. Using a loose variant of the circle method we sharpen this to $(e^{-1/2} + o(1)) n!^2 / n^n$. Our method works for all latin squares satisfying a certain quasirandomness condition, which includes both random latin squares with high probability as well as multiplication tables of quasirandom groups.
