ALIABADI-DISSERTATION-2020.pdf (302.68 kB)
Matchings in Groups and Vector Spaces
thesis
posted on 2020-08-01, 00:00 authored by Mohsen AliabadiA model for class of bipartite graphs is introduced, and a certain type of perfect matching,
called an acyclic matching, is defined to imply a nonvanishing determinant for a class of weighted
biadjacency matrices. Using the existence results in matching theory, an old linear algebra
problem on the removable sets of monomials from a generic homogenous polynomial through
linear changes in its variables is discussed.
The matching property defined in Zn is first generalized to abelian groups and later to
arbitrary groups. The local matching property is defined to give alternative proofs for existing
results in matching theory. Linear analogues of results concerning matchings in groups are
formulated and proven. Finally, an improvement of the fundamental theorem of algebra is
given as an application of matchings in field extensions.
History
Advisor
Friedland, ShmuelChair
Friedland, ShmuelDepartment
Mathematics , Statistics, and Computer ScienceDegree Grantor
University of Illinois at ChicagoDegree Level
- Doctoral
Degree name
PhD, Doctor of PhilosophyCommittee Member
Ein, Lawrence Turan , Gyorgy Perkins , William A. Brualdi, RichardSubmitted date
August 2020Thesis type
application/pdfLanguage
- en
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