On universal partial words

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Chen, Herman Z.Q. and Kitaev, Sergey and Mutze, Torsten and Sun, Brian Y. (2017) On universal partial words. Electronic Notes in Discrete Mathematics, 61. pp. 231-237. ISSN 1571-0653 (https://doi.org/10.1016/j.endm.2017.06.043)

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Abstract

A universal word for a finite alphabet A and some integer n≥1 is a word over A such that every word of length n appears exactly once as a (consecutive) subword. It is well-known and easy to prove that universal words exist for any A and n. In this work we initiate the systematic study of universal partial words. These are words that in addition to the letters from A may contain an arbitrary number of occurrences of a special ‘joker’ symbol ◊  A, which can be substituted by any symbol from A. For example, u = 0◊011100 is a universal partial word for the binary alphabet A = {0,1} and for n = 3 (e.g., the first three letters of u yield the subwords 000 and 010). We present several result on the existence and non-existence of universal partial words in different situations (depending on the number of ◊s and their positions), including various explicit constructions. We also provide numerous examples of universal partial words that we found with the help of a computer.

ORCID iDs

Chen, Herman Z.Q., Kitaev, Sergey ORCID logoORCID: https://orcid.org/0000-0003-3324-1647, Mutze, Torsten and Sun, Brian Y.;
  • Item type:Article
    ID code:60593
    Dates:
    Date
    Event
    31 August 2017
    Published
    3 August 2017
    Published Online
    29 April 2017
    Accepted
    Notes:© 2017 Elsevier B.V. All rights reserved. Herman Z.Q. Chen, Sergey Kitaev, Torsten Mütze, Brian Y. Sun, On universal partial words, Electronic Notes in Discrete Mathematics, Volume 61, 2017, Pages 231-237, https://doi.org/10.1016/j.endm.2017.06.043
    Subjects:Science > Mathematics
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:03 May 2017 13:30
    Last modified:11 Nov 2024 11:41
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/60593
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