JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (6): 11-15.doi: 10.6040/j.issn.1671-9352.0.2019.174

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

LIU Hai-yan, GUO Yu-qi*   

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu, China
  • Published:2019-06-05

Abstract: Let L be a nonempty language over A, k∈N0 and m∈N. If L satisfies (LAk)mL∩A+(LAk)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 2Xk\{Ø}, where Xk ={u∈A+|(∠w∈Ak)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 Xk for any k≥2.

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

CLC Number: 

  • O157.4
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