Generalized permutation patterns - a short survey

Research output: Contribution to journalArticle

Abstract

An occurrence of a classical pattern p in a permutation π is a
subsequence of π whose letters are in the same relative order (of size) as those
in p. In an occurrence of a generalized pattern, some letters of that subsequence
may be required to be adjacent in the permutation. Subsets of permutations
characterized by the avoidance—or the prescribed number of occurrences—
of generalized patterns exhibit connections to an enormous variety of other
combinatorial structures, some of them apparently deep. We give a short
overview of the state of the art for generalized patterns.
LanguageEnglish
Pages137–152
Number of pages16
JournalLondon Mathematical Society Lecture Note Series
Publication statusPublished - 2010

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Permutation
Adjacent
Subset

Keywords

  • permutation
  • pat- tern avoidance
  • Generalized permutation patterns
  • pattern

Cite this

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title = "Generalized permutation patterns - a short survey",
abstract = "An occurrence of a classical pattern p in a permutation π is asubsequence of π whose letters are in the same relative order (of size) as thosein p. In an occurrence of a generalized pattern, some letters of that subsequencemay be required to be adjacent in the permutation. Subsets of permutationscharacterized by the avoidance—or the prescribed number of occurrences—of generalized patterns exhibit connections to an enormous variety of othercombinatorial structures, some of them apparently deep. We give a shortoverview of the state of the art for generalized patterns.",
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Generalized permutation patterns - a short survey. / Steingrimsson, Einar.

In: London Mathematical Society Lecture Note Series, 2010, p. 137–152.

Research output: Contribution to journalArticle

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