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On uniquely k-determined permutations

Avgustinovich, Sergey and Kitaev, Sergey (2007) On uniquely k-determined permutations. In: 19th International Conference on Formal Power Series & Algebraic Combinatorics, 2007-07-02 - 2007-07-06, Nankai University.

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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 ¯nite 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.