On the Number of Rich Words

被引：7

作者：

Rukavicka, Josef ^{[1
]}

机构：

[1] Czech Tech Univ, Fac Nucl Sci & Phys Engn, Dept Math, Trojanova 13, Prague 12001 2, Czech Republic

来源：

DEVELOPMENTS IN LANGUAGE THEORY, DLT 2017 | 2017年 / 10396卷

关键词：

Rich words; Enumeration; Palindromes; Palindromic factorization; LANGUAGES;

D O I：

10.1007/978-3-319-62809-7_26

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Any finite word w of length n contains at most n + 1 distinct palindromic factors. If the bound n + 1 is reached, the word w is called rich. The number of rich words of length n over an alphabet of cardinality q is denoted R-q(n). For binary alphabet, Rubinchik and Shur deduced that R-2(n) <= c1.605(n) for some constant c. In addition, Guo, Shallit and Shur conjectured that the number of rich words grows slightly slower than n(root n). We prove that lim (n -> infinity) (n)root R-q(n) = 1 for any q, i.e. R-q(n) has a subexponential growth on any alphabet.

引用

页码：345 / 352

页数：8

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