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Alexander Valyuzhenich

  1. Permutation complexity of the fixed points of some uniform binary morphisms.

    Fri, 08/19/2011 - 15:01 — SomNambul
    Authors: Alexander Valyuzhenich
    Subjects: Discrete Mathematics
    Abstract

    An infinite permutation is a linear order on the set N. We study the
    properties of infinite permutations generated by fixed points of some uniform
    binary morphisms, and find the formula for their complexity.

  2. Two bijections for sets of words with forbidden factors.

    Tue, 11/03/2009 - 16:01 — SomNambul
    Authors: Alexander Valyuzhenich
    Subjects: Combinatorics
    Abstract

    In a recent paper by Kitaev and Remmel, several formulas for the number of
    words of length n avoiding some generalized patterns were established. Each
    time the obtained function of n had been found in Sloane's Encyclopedia as the
    number of some other objects, but the bijections between the two sets did not
    follow from the proof. Kitaev and Remmel stated four open problems on finding
    respective bijections. Here we solve two of them, concerning sequences A007070
    and A048739.

Math-arch

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