列举带有禁止因子的单词

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2019-03-01 DOI:10.1016/j.endm.2019.02.003

Richard Pinch

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引用次数: 0

摘要

本演示演示了递归关系理论在具有禁止因子(连续子字符串)的字母表上枚举字符串的应用。作为一个例子，我们研究了二进制字符串的情况，禁止因子为k个连续符号1，给定k，使用值得更好地了解的生成函数技术。这允许我们推导出前缀正常二进制单词数量的已知上界:具有相同长度的前缀中没有一个因子出现次数比符号1多的单词。这样的词出现在索引二进制混杂模式匹配的上下文中。

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Enumerating words with forbidden factors

This presentation is an exposition of an application of the theory of recurrence relations to enumerating strings over an alphabet with a forbidden factor (consecutive substring). As an illustration we examine the case of binary strings with a forbidden factor of k consecutive symbols 1 for given k, using generating function techniques that deserve to be better known.

This allows us to derive a known upper bound for the number of prefix normal binary words: words with the property that no factor has more occurrences of the symbol 1 than the prefix of the same length. Such words arise in the context of indexed binary jumbled pattern matching.

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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.