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    Notes on Foregger's conjecture

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    Melnykova_Kateryna.pdf (612.5Kb)
    Date
    2012-09-20
    Author
    Melnykova, Kateryna
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    Abstract
    This thesis is devoted to investigation of some properties of the permanent function over the set Omega_n of n-by-n doubly stochastic matrices. It contains some basic properties as well as some partial progress on Foregger's conjecture. CONJECTURE[Foregger] For every n\in N, there exists k=k(n)>1 such that, for every matrix A\in Omega_n, per(A^k)<=per(A). In this thesis the author proves the following result. THEOREM For every c>0, n\in N, for all sufficiently large k=k(n,c), for all A\in\Omega_n which minimum nonzero entry exceeds c, per(A^k)<=per(A). This theorem implies that for every A\in\Omega_n, there exists k=k(n,A)>1 such that per(A^k)<=per(A).
    URI
    http://hdl.handle.net/1993/8893
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    • FGS - Electronic Theses and Practica [25494]

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