关于1-(k,m)-逗点码的一个注记

doi:10.6040/j.issn.1671-9352.0.2019.174

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (6): 11-15.doi: 10.6040/j.issn.1671-9352.0.2019.174

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关于1-(k,m)-逗点码的一个注记

刘海艳,郭聿琦^*

兰州大学数学与统计学院, 甘肃兰州 730000

发布日期:2019-06-05
作者简介:LIU Hai-yan(1985— ), Female, PhD.Student, Associate Professor, Her research interests mainly include combinatorial semigroups. E-mail: liuhy16@lzu.edu.cn*Communication author
基金资助:
SupportedbyNationalNaturalScienceFoundationofChina(11861051)

Anote-on-1-(k,m)-comma-codes ——several studies on combinatorial semigroups(Ⅲ)

LIU Hai-yan, GUO Yu-qi^*

School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu, China

Published:2019-06-05

摘要/Abstract

摘要： 令L是A上的一个非空语言,k∈N⁰, m∈N。如果L满足(LA^k)^mL∩A⁺(LA^k)^m-1LA⁺=Ø,那么L是一个码,叫做(k,m)-逗号码。如果L的每个单点集都是一个(k,m)-逗号码,那么L称为1-(k,m)-逗号码。众所周知,1-(k,m)-逗号码类是2^Xk\{Ø},其中X_k ={u∈A⁺|(∠w∈A^k)uwu∩A⁺uA⁺=Ø}。 Jürgensen等指出X₀是本原字构成之集。 Cui等借助于有界字、无界字和本原字刻画了X₁。本文中,我们讨论X_k,其中k≥2。

关键词: 字的组合, (k,m)-逗号码, 1-(k,m)-逗号码

Abstract: Let L be a nonempty language over A, k∈N⁰ and m∈N. If L satisfies (LA^k)^mL∩A⁺(LA^k)^m-1LA⁺=Ø, then it is a code called (k,m)-comma code. If every singleton of L is a (k,m)-comma code, then it is called a 1-(k,m)-comma code. It is known that the class of 1-(k,m)-comma code is 2^Xk\{Ø}, where X_k ={u∈A⁺|(∠w∈A^k)uwu∩A⁺uA⁺=Ø}. Jürgensen et al. showed that X0 is the set of primitive words. Cui et al. gave a characterization of X1 in terms of bordered words, unbordered words, and primitive words. In this paper, we discuss X_k for any k≥2.

Key words: combinatorics of words, (k,m)-comma code, 1-(k,m)-comma code

中图分类号:

O157.4

刘海艳,郭聿琦. 关于1-(k,m)-逗点码的一个注记[J]. 《山东大学学报(理学版)》, 2019, 54(6): 11-15.

LIU Hai-yan, GUO Yu-qi. Anote-on-1-(k,m)-comma-codes ——several studies on combinatorial semigroups(Ⅲ)[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 11-15.

参考文献

[1] BERSTEL J, PERRIN D. Theory of codes[M]. Orlando: Academic Press, 1985.
[2] ROZENBERG G. Handbook of formal languages[M] // SALOMAA A. Word, Language, Grammar, Vol.1. Berlin: Springer, 1997.
[3] CAO C H, LIU H Y, YANG D. Characterizations of k-comma codes and k-comma intercodes[J]. Acta Inf, 2016, 53:23-33.
[4] CUI B, KARI L, SEKI S. k-comma codes and their generalizations[J]. Fund Inf, 2011, 107:1-18.
[5] JÜRGENSEN H, YU S S. Relations on free monoids, their independent sets, and codes[J]. Intern J Computer Math, 1991, 40:17-46.
[6] SHYR H J. Free monoids and languages[M]. 3rd. [S.l.] : Hon Min Book Company, 2001.

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关于1-(k,m)-逗点码的一个注记

Anote-on-1-(k,m)-comma-codes ——several studies on combinatorial semigroups(Ⅲ)

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