Enumerating words with forbidden factors

Q2 Mathematics

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

Richard Pinch

引用次数: 0

Abstract

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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列举带有禁止因子的单词

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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

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