Show simple item record

dc.contributor.advisorRiener, Cordian
dc.contributor.advisorMoustrou, Philippe
dc.contributor.authorLien, Arne
dc.date.accessioned2021-07-02T06:34:14Z
dc.date.available2021-07-02T06:34:14Z
dc.date.issued2021-05-14en
dc.description.abstractPolynomials appear in many different fields such as statistics, physics and optimization. However, when the degrees or the number of variables are high, it generally becomes quite difficult to solve polynomials or to optimize polynomial functions. An approach that can often be helpful to reduce the complexity of such problems is to study symmetries in the problems. A relatively new field, that has gained a lot of traction in the last fifteen years, is the study of symmetry in polynomial rings in increasingly many variables. By considering the action of the symmetric groups on these polynomial rings, one can for instance show that certain sequences of symmetric ideals in increasingly larger polynomial rings are finitely generated up to orbits. In this thesis we will investigate some properties of such sequences. In particular the Hilbert Series and Gröbner bases of Specht ideals, a class of ideals arising from the representation theory of the symmetric group. We prove a conjectured Gröbner basis for Specht ideals of shape (n−k, 1^k) and give two different criteria for verifying the conjecture for other Specht ideals. We also build on a result from the representation theory of the symmetric group by showing that the leading monomials of the standard Specht polynomials span the vector space of leading monomials of Specht polynomials.en_US
dc.identifier.urihttps://hdl.handle.net/10037/21686
dc.language.isoengen_US
dc.publisherUiT Norges arktiske universitetno
dc.publisherUiT The Arctic University of Norwayen
dc.rights.holderCopyright 2021 The Author(s)
dc.rights.urihttps://creativecommons.org/licenses/by-nc-sa/4.0en_US
dc.rightsAttribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)en_US
dc.subject.courseIDMAT-3900
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Algebra/algebraisk analyse: 414en_US
dc.subjectVDP::Mathematics and natural science: 400::Mathematics: 410::Algebra/algebraic analysis: 414en_US
dc.titleSymmetric Idealsen_US
dc.typeMastergradsoppgavenor
dc.typeMaster thesiseng


File(s) in this item

Thumbnail
Thumbnail

This item appears in the following collection(s)

Show simple item record

Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)