Separable d-permutations and guillotine partitions

Andrei Asinowski, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


We characterize separable multidimensional permutations in terms of forbidden patterns and enumerate them by means of generating function, recursive formula, and explicit formula. We find a connection between multidimensional permutations and guillotine partitions of a box. In particular, a bijection between separable d-dimensional permutations and guillotine partitions of a 2d-1-dimensional box is constructed. We also study enumerating problems related to guillotine partitions under certain restrictions revealing connections to other combinatorial structures. This allows us to obtain several results on patterns in permutations.

Original languageEnglish
Pages (from-to)17-43
Number of pages27
JournalAnnals of Combinatorics
Issue number1
StatePublished - Mar 2010


  • Binary trees
  • Guillotine partitions
  • Patterns in permutations
  • Schröder paths
  • Separable permutations
  • d-permutations

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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