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).
| Identifer | oai:union.ndltd.org:MANITOBA/oai:mspace.lib.umanitoba.ca:1993/8893 |
| Date | 20 September 2012 |
| Creators | Melnykova, Kateryna |
| Contributors | Kopotun, Kirill (Mathematics), Gunderson, David (Mathematics) Brewster, John (Statistics) |
| Source Sets | University of Manitoba Canada |
| Detected Language | English |
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