Inequalities characterizing standard Sturmian and episturmian words

被引：15

作者：

Pirillo, G

机构：

[1] Univ Florence, Dipartimento Matemat U Dini, CNR, IASI, I-50134 Florence, Italy

[2] Univ Marne La Vallee, F-77454 Marne La Vallee, France

来源：

THEORETICAL COMPUTER SCIENCE | 2005年 / 341卷 / 1-3期

关键词：

words; lexicographic order; infinite words; Sturmian words; Episturmian words;

D O I：

10.1016/j.tcs.2005.04.008

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Considering the smallest and the greatest factors with respect to the lexicographic order we associate to each infinite word r two other infinite words min(r) and max(r). In this paper we prove that the inequalities as <= min(s) <= max(s) <= bs characterize standard Sturmian words (proper ones and periodic ones) and that the condition "for any x is an element of A and lexicographic order < satisfying x = min (A) one has xs <= min(s)" characterizes standard episturmian words. (c) 2005 Elsevier B.V. All rights reserved.

引用

页码：276 / 292

页数：17

共 17 条

[1]

Borel J.-P., 1993, J THEOR NOMBRES BORD, V5, P23

[2]

Christoffel E.B., 1875, ANN MAT PUR APPL, V6, P145

[3] Sturmian words: structure, combinatorics, and their arithmetics [J].