算术推进后缀数组及其相关Burrows-Wheeler变换
On Arithmetically Progressed Suffix Arrays and related Burrows-Wheeler Transforms
摘要：
我们的特点是这些字符串的后缀数组是基于等差数列，特别是，算术进展的置换，其中所有对连续条目的置换具有相同的差异模各自的字符串长度。我们表明，算术进展置换$P$符合后缀数组的一元，二进制或三进制字符串。我们进一步分析了一个给定的$P$的条件下，我们可以找到一个唯一定义的字符串，无论是二进制或三进制字母表有$P$作为其后缀数组。对于二进制的情况下，我们将其连接到较低的克里斯托弗的话，平衡的话，斐波那契的话。除了解决算术进展后缀数组问题，我们给出了解决这个问题的字符串的Burrows-Wheeler变换的形状。这些结果为今后的研究指明了方向。
英文摘要：
We characterize those strings whose suffix arrays are based on arithmetic progressions, in particular, arithmetically progressed permutations where all pairs of successive entries of the permutation have the same difference modulo the respective string length. We show that an arithmetically progressed permutation $P$ coincides with the suffix array of a unary, binary, or ternary string. We further analyze the conditions of a given $P$ under which we can find a uniquely defined string over either a binary or ternary alphabet having $P$ as its suffix array. For the binary case, we show its connection to lower Christoffel words, balanced words, and Fibonacci words. In addition to solving the arithmetically progressed suffix array problem, we give the shape of the Burrows-Wheeler transform of those strings solving this problem. These results give rise to numerous future research directions.
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