Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 6 (2019), 901-918.

Occurrence graphs of patterns in permutations

Bjarni Jens Kristinsson and Henning Ulfarsson

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We define the occurrence graph Gp(π) of a pattern p in a permutation π as the graph whose vertices are the occurrences of p in π, with edges between the vertices if the occurrences differ by exactly one element. We then study properties of these graphs. The main theorem in this paper is that every hereditary property of graphs gives rise to a permutation class.

Article information

Involve, Volume 12, Number 6 (2019), 901-918.

Received: 11 July 2016
Revised: 15 February 2019
Accepted: 18 February 2019
First available in Project Euclid: 13 August 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05A05: Permutations, words, matrices 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 05C30: Enumeration in graph theory

graph permutation subgraph pattern


Kristinsson, Bjarni Jens; Ulfarsson, Henning. Occurrence graphs of patterns in permutations. Involve 12 (2019), no. 6, 901--918. doi:10.2140/involve.2019.12.901.

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  • P. Brändén and A. Claesson, “Mesh patterns and the expansion of permutation statistics as sums of permutation patterns”, Electron. J. Combin. 18:2 (2011), art. id. 5.
  • A. Claesson, B. E. Tenner, and H. Ulfarsson, “Coincidence among families of mesh patterns”, Australas. J. Combin. 63 (2015), 88–106.
  • L. Comtet, Advanced combinatorics: the art of finite and infinite expansions, enlarged ed., Reidel, Dordrecht, 1974.
  • P. Erdős and G. Szekeres, “A combinatorial problem in geometry”, Compositio Math. 2 (1935), 463–470.
  • S. Kitaev, Patterns in permutations and words, Springer, 2011.
  • D. E. Knuth, The art of computer programming, I: Fundamental algorithms, Addison-Wesley, Boston, 1968.
  • P. A. MacMahon, Combinatory analysis, I, Cambridge Univ. Press, 1915.
  • H. Magnusson and H. Ulfarsson, “Algorithms for discovering and proving theorems about permutation patterns”, preprint, 2012.