On uniquely k-determined permutations

Sergey Avgustinovich, Sergey Kitaev

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


Motivated by a new point of view to study occurrences of consecutive patterns in permutations, we introduce the notion of uniquely k-determined permutations. We give two criteria for a permutation to be uniquely k-determined: one in terms of the distance between two consecutive elements in a permutation, and the other one in terms of directed hamiltonian paths in the certain graphs called path-schemes. Moreover, we describe a finite set of prohibitions that gives the set of uniquely k-determined permutations. Those prohibitions make the application of the transfer matrix method possible for determining the number of uniquely k-determined permutations.
Original languageEnglish
Pages (from-to)1500-1507
Number of pages8
JournalDiscrete Mathematics
Issue number9
Early online date6 Apr 2007
Publication statusPublished - May 2008


  • de Bruijn graph
  • consecutive pattern
  • set of prohibitions
  • permutations
  • reconstruction


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