Some results on the avoidance of vincular patterns by multisets

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 must satisfy an adjacency requirement. In this paper, we show some general equivalences concerning the avoidance of vincular patterns by multiset permutations. We prove our results by defining bijections between various avoidance classes that preserve the number of occurrences of each letter. As a consequence, we obtain for multiset permutations the complete Wilf-classification of patterns of type (2,1,1), which also yields the complete classification for compositions and k-ary words when taken with numerical evidence.

Original languageEnglish
Pages (from-to)201-208
Number of pages8
JournalDiscrete Applied Mathematics
StatePublished - 30 Jan 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier B.V. All rights reserved.


  • Multiset permutation
  • Pattern avoidance
  • Vincular patterns

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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