论文标题
差异差异的分布
Distribution of missing differences in diffsets
论文作者
论文摘要
Lazarev，Miller和O'Bryant调查了$ | S+S | $的分布，$ s $从$ \ {0，1，1，\ dots，n-1 \} $中随机选择，证明存在7和缺少7总和的可能性（丢失的7和少于缺少6或缺少8和丢失8和）。我们研究了$ | s-s | $的相关问题，并显示了概率分布的一端的一些分离，$ p（| s-s | = k）$，以及另一端的$ k = 4 $的峰值，$ p（2n-1- | s-s | = k）$。我们的结果的推论是对长度$ n $的完整统治者的数量的渐近线。
Lazarev, Miller and O'Bryant investigated the distribution of $|S+S|$ for $S$ chosen uniformly at random from $\{0, 1, \dots, n-1\}$, and proved the existence of a divot at missing 7 sums (the probability of missing exactly 7 sums is less than missing 6 or missing 8 sums). We study related questions for $|S-S|$, and shows some divots from one end of the probability distribution, $P(|S-S|=k)$, as well as a peak at $k=4$ from the other end, $P(2n-1-|S-S|=k)$. A corollary of our results is an asymptotic bound for the number of complete rulers of length $n$.
