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Enumerating Abelian Returns to Prefixes of Sturmian Words

机译：枚举Abelian返回Sturmian词的前缀

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We follow the works of Puzynina and Zamboni, and Rigo et al. on abelian returns in Sturmian words. We determine the cardinality of the set APR_U of abelian returns of all prefixes of a Sturmian word u in terms of the coefficients of the continued fraction of the slope, dependingly on the intercept. We provide a simple algorithm for finding the set APR_u and we determine it for the characteristic Sturmian words.

机译：我们关注Puzynina和Zamboni以及Rigo等人的工作。以阿斯图里亚斯（Aturian）的单词表示阿贝尔语。我们根据斜率的连续部分的系数，确定Sturmian单词u的所有前缀的阿贝尔返回的集合APR_U的基数，具体取决于截距。我们提供了一种简单的算法来查找集合APR_u，并针对特征性Sturmian单词对其进行确定。

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来源
《Combinatorics on words》|2013年|193-204|共12页
会议地点 Turku(FI)
作者
Zuzana Masakova; Edita Pelantova;
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作者单位

Department of Mathematics FNSPE, Czech Technical University in Prague Trojanova 13, 120 00 Praha 2, Czech Republic;

Department of Mathematics FNSPE, Czech Technical University in Prague Trojanova 13, 120 00 Praha 2, Czech Republic;

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原文格式 PDF
正文语种 eng
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关键词
Abelian return word; Sturmian word; interval exchange;

机译：阿拉伯语返回字；突厥词间隔交换;

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专利

1. Vacuum-Induced Abelian and Non-Abelian Gauge Potentials in Cavity Quantum Electrodynamics [J] . 张海龙, 梁奇锋, 俞立先, 理论物理通讯（英文版） . 2011,第012期
2. Abelian returns in Sturmian words [J] . Puzynina S., Zamboni L.Q. Journal of Combinatorial Theory, Series A . 2013,第2期

机译：阿伯利亚文用Sturmian的话返回
3. The sequence of open and closed prefixes of a Sturmian word [J] . De Luca Alessandro, Fici Gabriele, Zamboni Luca Q. Advances in Applied Mathematics . 2017,第期

机译：Sturmian词的开放和封闭前缀的顺序
4. Abelian powers and repetitions in Sturmian words [J] . Fici Gabriele, Langiu Alessio, Lecroq Thierry, Theoretical computer science . 2016,第Null期

机译：阿斯图里亚斯语单词中的阿贝尔力量和重复
5. Enumerating Abelian Returns to Prefixes of Sturmian Words [C] . Zuzana Masakova, Edita Pelantova International Conference on Combinatorics on Words . 2013

机译：枚举abelian返回Strmian词的前缀
6. Sturmian dynamical systems. [D] . Hillman, Chris. 1998

机译：Sturmian动力系统。
7. Enumeration of the Abelian Groups Whose Orders Do Not Exceed a Given Number [O] . G. A. Miller 1936

机译：顺序不超过给定数目的阿贝尔群的枚举
8. Enumerating Abelian Returns to Prefixes of Sturmian Words [O] . 2016

机译：枚举abelian返回sturmian词的前缀

Enumerating Abelian Returns to Prefixes of Sturmian Words

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