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Notes on Foregger's conjecture

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).

Identiferoai:union.ndltd.org:MANITOBA/oai:mspace.lib.umanitoba.ca:1993/8893
Date20 September 2012
CreatorsMelnykova, Kateryna
ContributorsKopotun, Kirill (Mathematics), Gunderson, David (Mathematics) Brewster, John (Statistics)
Source SetsUniversity of Manitoba Canada
Detected LanguageEnglish

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