Notes on Foregger's conjecture
| dc.contributor.author | Melnykova, Kateryna | |
| dc.contributor.examiningcommittee | Gunderson, David (Mathematics) Brewster, John (Statistics) | en_US |
| dc.contributor.supervisor | Kopotun, Kirill (Mathematics) | en_US |
| dc.date.accessioned | 2012-09-20T15:27:45Z | |
| dc.date.available | 2012-09-20T15:27:45Z | |
| dc.date.issued | 2012-09-20 | |
| dc.degree.discipline | Mathematics | en_US |
| dc.degree.level | Master of Science (M.Sc.) | en_US |
| dc.description.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). | en_US |
| dc.description.note | October 2012 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/8893 | |
| dc.language.iso | eng | en_US |
| dc.rights | open access | en_US |
| dc.subject | permanent | en_US |
| dc.subject | linear algebra | en_US |
| dc.subject | doubly stochastic matrix | en_US |
| dc.title | Notes on Foregger's conjecture | en_US |
| dc.type | master thesis | en_US |