On Arithmetic Index in the Generalized Thue-Morse Word
On Arithmetic Index in the Generalized Thue-Morse Word
复制标题
广义Thue-Morse字中的算术索引
DOI：
--
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
O. Parshina
中科院分区：
文献类型：
--
作者：
O. Parshina
设q为正整数。考虑无限词(ω= w_0w_1w_2cdots)基数q。一个有限的单词的字母u叫做等差因子(ω)如果(u = w_cw_ {c + d} w_ {c + 2 d} cdots w_ {c + d (u | | 1)})对于一些正整数c和d的选择。我们称之为c最初的数量和d u的区别。对于每一次这样的你我们定义其算术指数(lceil日志_q d装天花板),d是最小正整数,你出现在(ω)作为一个算术因素与不同d。在本文中,我们研究在素数基数的字母表上定义的Thue-Morse字的泛化的算术因子的算术指数的增长率。更精确地说，我们得到了（ω）中所有长度为n的算术因子中算术指标最大值的上界和下界。
Let q be a positive integer. Consider an infinite word (omega =w_0w_1w_2cdots ) over an alphabet of cardinality q. A finite word u is called an arithmetic factor of (omega ) if (u=w_cw_{c+d}w_{c+2d}cdots w_{c+(|u|-1)d}) for some choice of positive integers c and d. We call c the initial number and d the difference of u. For each such u we define its arithmetic index by (lceil log _q d
ceil ) where d is the least positive integer such that u occurs in (omega ) as an arithmetic factor with difference d. In this paper we study the rate of growth of the arithmetic index of arithmetic factors of a generalization of the Thue-Morse word defined over an alphabet of prime cardinality. More precisely, we obtain upper and lower bounds for the maximum value of the arithmetic index in (omega ) among all its arithmetic factors of length n.