Picture of neon light reading 'Open'

Discover open research at Strathprints as part of International Open Access Week!

23-29 October 2017 is International Open Access Week. The Strathprints institutional repository is a digital archive of Open Access research outputs, all produced by University of Strathclyde researchers.

Explore recent world leading Open Access research content this Open Access Week from across Strathclyde's many research active faculties: Engineering, Science, Humanities, Arts & Social Sciences and Strathclyde Business School.

Explore all Strathclyde Open Access research outputs...

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)

[img] Text (Chen-etal-ENDM-2017-On-universal-partial-words)
Chen_etal_ENDM_2017_On_universal_partial_words.pdf - Accepted Author Manuscript
Restricted to Repository staff only until 3 May 2018.
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo

Download (347kB) | Request a copy from the Strathclyde author


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.