On avoidance of patterns of the form σ-τ By words over a finite alphabet

Toufik Mansour, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


Vincular or dashed patterns resemble classical patterns except that some of the letters within an occurrence are required to be adjacent. We prove several infinite families of Wilf-equivalences for k-ary words involving vincular patterns containing a single dash, which explain the majority of the equivalences witnessed for such patterns of length four. When combined with previous results, numerical evidence, and some arguments in specific cases, we obtain the complete Wilf-classification for all vincular patterns of length four containing a single dash. In some cases, our proof shows further that the equivalence holds for multiset permutations since it is seen to respect the number of occurrences of each letter within a word. Some related enumerative results are provided for patterns τ of length four, among them generating function formulas for the number of members of [k]n avoiding any τ of the form 11a-b.

Original languageAmerican English
Pages (from-to)181-202
Number of pages22
Issue number2
StatePublished - 2015


  • K-ary words
  • Pattern avoidance
  • Vincular patterns

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science
  • Discrete Mathematics and Combinatorics


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