论文标题
Burdzy-Pitman猜想的组合证明
A combinatorial proof of the Burdzy-Pitman conjecture
论文作者
论文摘要
我们证明了两部分图的高度差异的尖锐上限：让$（u，v，e）$是一个带有$ u = \ = \ {u_1，u_2，\ dots，u_n \} $ and u_n \} $和$ v = \ \ \ \ \ {v_1，v_1，v_2，v_2，v_2，v_2，dots，v_n p，v_n p，v_n \ v_n \} $ u_n \} $的两部分图形图对于$ n \ ge k> \ frac {n} {2} $，我们表明$ \ sum_ {1 \ le i，j \ le n} 1 {\ big \ \ {| \ text {deg} {deg}（u_i） - \ text {deg}（v_j）该定理的更强，更概率的版本，因此证实了关于连贯和独立分布的最大传播的顽强的猜想。
We prove a sharp upper bound for the number of high degree differences in bipartite graphs: let $ (U, V, E)$ be a bipartite graph with $U=\{u_1, u_2, \dots, u_n\}$ and $V=\{v_1, v_2, \dots, v_n\}$; for $n\ge k>\frac{n}{2}$ we show that $\sum_{1\le i,j \le n} 1 {\Big\{|\text{deg}(u_i)-\text{deg}(v_j)|\ge k}\Big\} \le 2k(n-k).$ As a direct application we show a slightly stronger, probabilistic version of this theorem and thus confirm the Burdzy-Pitman conjecture about the maximal spread of coherent and independent distributions.
