Sets of period sets for words of length n.

We consider finite words of length n. Each word has a set of periods, but many words can have the same set of periods. For a definition of a period of a word, see [1]. A set of periods is a subset of the set {0, 1, ..., n-1}, but not all subsets of {0, 1, ..., n-1} are period sets. The set denoted Gamma(n) contains all possible period sets corresponding to at least one word of length n. For a definition of Gamma(n), see references [1] or [2]. For more details see reference [4]. The series of text files provide the list of period set, one per line, for Gamma(n), for n = 1, 2, ..., 100.Each line contains a list of integers sorted by increasing value: this list constitutes one period set. The separator symbol is a space. Hence, the number of non-empty lines in a file gives the cardinality of Gamma(n).The period set are sorted by their basic period. For a definition of the notion of basic period, see [1] or [2]. The files for n=61, ..., 100, where computed with the incremental algorithm described in [5]. The sequence of the cardinalities of the set Gamma(n), is also called, the Number of distinct autocorrelations of binary words of length n, and corresponds to the sequence A005434 in the Encyclopedia of Integer Sequences (EOIS) link [3]. The files have generic name formatted as follows: gamma.n.bpswhere n is the word length, for n = 1, 2, ..., 100. References: 1. Eric Rivals, Sven Rahmann. Combinatorics of Periods in Strings. Proc. 28th International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science vol. 2076, p. 615-26., P. Orejas, P. G. Spirakis, J. van Leuween editors, Springer Verlag, Berlin, 2001. doi: https://doi.org/10.1007/3-540-48224-5_512. Eric Rivals, Sven Rahmann. Combinatorics of Periods in Strings. Journal of Combinatorial Theory - Series A, 104(1), p. 95-113, October 2003 doi: https://doi.org/10.1016/s0097-3165(03)00123-73. Entry A005434 from The On-Line Encyclopedia of Integer Sequences. URL: https://oeis.org/A0054344. Autocorrelation of Strings. A comment on entries A005434 and A045690 of the Encyclopedia of Integer Sequences. URL: https://www.lirmm.fr/~rivals/RESEARCH/PERIOD/ 5. Eric Rivals. Incremental computation of the set of period sets. arXiv:2410.12077, 2024. https://doi.org/10.48550/arXiv.2410.12077我们研究长度为n的有限字（finite words）。每个有限字都对应一个周期集（period set），但多个不同的有限字可共享同一周期集。关于字的周期的定义，请参见文献[1]。周期集是集合{0, 1, …, n−1}的子集，但并非该集合的所有子集均为合法周期集。记为Gamma(n)的集合包含所有至少对应一个长度为n的有限字的周期集。关于Gamma(n)的定义，请参见文献[1]或[2]，更多细节可参阅文献[4]。 本系列文本文件给出了n=1, 2, …, 100时Gamma(n)的所有周期集列表，每个周期集占一行。每行包含按升序排列的整数列表，该列表即对应一个周期集，分隔符为空格。因此，文件中非空行的数量即为Gamma(n)的基数（cardinality）。所有周期集均按其基本周期（basic period）排序，关于基本周期的定义，请参见文献[1]或[2]。 n=61至100对应的文件是通过文献[5]中描述的增量算法（incremental algorithm）计算得到的。 Gamma(n)的基数序列也被称为“长度为n的二进制字（binary words）的不同自相关数”，对应整数序列百科全书（Encyclopedia of Integer Sequences, EOIS）中的A005434序列，详见链接[3]。 文件的通用命名格式如下：gamma.n.bps，其中n为有限字的长度，取值范围为1至100。 参考文献： 1. Eric Rivals、Sven Rahmann. 字符串中的周期组合学[C]. 第28届国际自动机、语言和程序设计大会论文集，《计算机科学讲义》（Lecture Notes in Computer Science）卷2076，第615-626页，P. Orejas、P. G. Spirakis、J. van Leuwen 编辑，Springer Verlag，柏林，2001. DOI: https://doi.org/10.1007/3-540-48224-5_512 2. Eric Rivals、Sven Rahmann. 字符串中的周期组合学[J]. 《组合理论杂志A辑》（Journal of Combinatorial Theory - Series A），104(1)，第95-113页，2003年10月. DOI: https://doi.org/10.1016/s0097-3165(03)00123-73 3. 整数序列在线百科全书A005434条目. 网址：https://oeis.org/A0054344 4. 字符串自相关：关于整数序列百科全书A005434与A045690条目的评论. 网址：https://www.lirmm.fr/~rivals/RESEARCH/PERIOD/ 5. Eric Rivals. 周期集的增量计算[EB/OL]. arXiv:2410.12077, 2024. DOI: https://doi.org/10.48550/arXiv.2410.12077