On universal partial words
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: https://orcid.org/0000-0003-3324-1647, Mutze, Torsten and Sun, Brian Y.;-
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Item type: Article ID code: 60593 Dates: DateEvent31 August 2017Published3 August 2017Published Online29 April 2017AcceptedNotes: © 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: 22 Oct 2024 00:24 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/60593