Buck，Chan和Robbins关于随机分配问题的一个猜想的证明
A proof of a conjecture of Buck, Chan and Robbins on the random assignment problem
摘要：
本文证明了Marshall W. Buck，Clara S. Chan和David P. Robbins（Random Structures & Algorithms 21（2002），no.1，33- 58）。这是Giorgio Parisi为$n$乘$n$随机分配问题所建立的一个公式的广泛推广。我们结合了Buck，Chan和Robbins的文章中的瓮模型，以及今年3月在Arxiv上发表的文章中对Parisi猜想的证明。我们的新定理同时推广了文章中的主要定理和Buck，Chan和Robbins的猜想。使用瓮模型，我们避免了一些技术上的困难，从我们以前的证明帕里西的猜想，并得到一个较短的证明在一个概念上更吸引人的设置。
英文摘要：
We prove the main conjecture of the paper ``On the expected value of the minimum assignment'' by Marshall W. Buck, Clara S. Chan, and David P. Robbins (Random Structures & Algorithms 21 (2002), no. 1, 33--58). This is a vast generalization of a formula conjectured by Giorgio Parisi for the $n$ by $n$ random assignment problem. We combine the urn model from the article by Buck, Chan and Robbins, with our proof of Parisi's conjecture in our article posted on the Arxiv in March this year. Our new theorem generalize simultaneously our main theorem from that article and the conjecture by Buck, Chan and Robbins. Using the urn model we avoid several technical difficulties from our previous proof of Parisi's conjecture and get a shorter proof in a conceptually more appealling setting.
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