RAIRO-Theor. Inf. Appl.
Volume 54, 2020
|Number of page(s)||14|
|Published online||04 June 2020|
On universal partial words for word-patterns and set partitions
School of Statistics and Data Science, Nankai University, PR China.
2 Department of Mathematics and Statistics, University of Strathclyde, UK.
* Corresponding author: email@example.com
Accepted: 10 March 2020
Universal words are words containing exactly once each element from a given set of combinatorial structures admitting encoding by words. Universal partial words (u-p-words) contain, in addition to the letters from the alphabet in question, any number of occurrences of a special “joker” symbol. We initiate the study of u-p-words for word-patterns (essentially, surjective functions) and (2-)set partitions by proving a number of existence/non-existence results and thus extending the results in the literature on u-p-words and u-p-cycles for words and permutations. We apply methods of graph theory and combinatorics on words to obtain our results.
Mathematics Subject Classification: 68R15
Key words: universal word / partial word / set partition / word-pattern / De Bruijn graph / Eulerian path / Hamiltonian path
© EDP Sciences, 2020
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