On unavoidable sets of word patterns

Alexander Burstein, Sergey Kitaev

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern overlaps introduced in this paper, which is a subgraph of the de Bruijn graph and which we prove to be Hamiltonian. In other cases we reduce a problem under consideration to known facts on unavoidable sets of words. We also give a relation between our problem and intensively studied universal cycles, and prove there exists a universal cycle for word patterns of any length over any alphabet.
Original languageEnglish
Pages (from-to)371-381
Number of pages11
JournalSIAM Journal on Discrete Mathematics
Volume19
Issue number2
DOIs
Publication statusPublished - 2005

Keywords

  • word pattern
  • universal cycles
  • de Bruijn graph
  • (un)avoidability

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