On universal partial words for word-patterns and set partitions

Herman Z. Q. Chen, Sergey Kitaev

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Universal words are words containing exactly once each element from a given set of combinatorial structures admiting 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.
Original languageEnglish
Article number5
Number of pages14
JournalRAIRO - Theoretical Informatics and Applications (RAIRO: ITA)
Publication statusPublished - 4 Jun 2020


  • universal word
  • partial word
  • set partition
  • word-pattern
  • De Bruijn graph
  • Eulerian path
  • Hamiltonian path


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