随机修饰效应的波动的大小的LCS的两个序列的i.i.d.块
Random modification effect in the size of the fluctuation of the LCS of two sequences of i.i.d. blocks
摘要：
两个独立序列的最长公共子序列（LCS）的涨落的阶数问题已经公开了几十年。关于这一问题，存在着Chvatal-Sankoff（1975）和Waterman（1994）的两种相互矛盾的观点.在本文中，我们考虑一个特殊的模型的独立同分布。由积木组成的序列。一个块是一个连续的子串，只包含一种类型的符号。我们的模型只允许三种可能的分组长度，每一种都是等概率选取的。在这种情况下，我们引入一个随机操作（随机修改）的序列之一的块。在本文中，我们开发的技术来证明以下内容：如果我们假设的随机修改增加了LCS的长度以高概率，那么LCS的涨落的顺序是由Waterman所证明的。这一结果是研究i.i.d.序列LCS涨落大小的关键技术部分。由Matzinger和Torres开发。
英文摘要：
The problem of the order of the fluctuation of the Longest Common Subsequence (LCS) of two independent sequences has been open for decades. There exist contradicting conjectures on the topic, due to Chvatal - Sankoff in 1975 and Waterman in 1994. In the present article, we consider a special model of i.i.d. sequences made out of blocks. A block is a contiguous substring consisting only of one type of symbol. Our model allows only three possible block lengths, each been equiprobable picked up. In this context, we introduce a random operation (random modification) on the blocks of one of the sequences. In the present article, we develop the techniques to prove the following: if we suppose that the random modification increases the length of the LCS with high probability, then the order of the fluctuation of the LCS is as conjectured by Waterman. This result is a key technical part in the study of the size of the fluctuation of the LCS for sequences of i.i.d. blocks, developed by Matzinger and Torres.
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