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. ISSN 1571-0653 (In Press)

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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.

Author(s):	Chen, Herman Z.Q., Kitaev, Sergey ORCID: https://orcid.org/0000-0003-3324-1647, Mutze, Torsten and Sun, Brian Y.
Item type:	Article
ID code:	60593
Keywords:	universal words, joker symbol, binary alphabet, Mathematics, Discrete Mathematics and Combinatorics
Subjects:	Science > Mathematics
Department:	Faculty of Science > Computer and Information Sciences
Depositing user:	Pure Administrator
Date deposited:	03 May 2017 13:30
Last modified:	09 Jan 2020 00:08
Related URLs:	Event Journal or Publication
URI:	https://strathprints.strath.ac.uk/id/eprint/60593
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