Wilf-equivalence on k-ary words, compositions, and parking functions

Vít Jelínek, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


In this paper we study pattern-avoidance in the set of words over the alphabet [κ].We say that a word w∈[κ]ncontains a pattern t ∈ [ℓ]mif ω contains a subsequence order-isomorphic to τ . This notion generalizes pattern-avoidance in permutations. We determine all the Wilf-equivalence classes of wordpatterns of length at most six. We also consider analogous problems within the set of integer compositions and the set ofparking functions, which may both be regarded as special types of words, and which contain all permutations. In both theserestricted settings, we determine the equivalence classes of all patterns of length at most five. As it turns out, the fullclassification of these short patterns can be obtained with only a few general bijective arguments, which are applicable topatterns of arbitrary size.

Original languageEnglish
Article numberR60
JournalElectronic Journal of Combinatorics
Issue number1
StatePublished - 11 May 2009

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


Dive into the research topics of 'Wilf-equivalence on k-ary words, compositions, and parking functions'. Together they form a unique fingerprint.

Cite this