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Representations From Group Actions On Words And MatricesAnderson, Joel T 01 June 2023 (has links) (PDF)
We provide a combinatorial interpretation of the frequency of any irreducible representation of Sn in representations of Sn arising from group actions on words. Recognizing that representations arising from group actions naturally split across orbits yields combinatorial interpretations of the irreducible decompositions of representations from similar group actions. The generalization from group actions on words to group actions on matrices gives rise to representations that prove to be much less transparent. We share the progress made thus far on the open problem of determining the irreducible decomposition of certain representations of Sm × Sn arising from group actions on matrices.
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Symmetric Lorentzian polynomials / symmetriska lorentziska polynomQin, Daniel January 2023 (has links)
In 2020, Huh, Matherne, Mészáros, and St. Dizier established the Lorentzian property of normalized Schur polynomials and conjectured the Lorentzian nature of other Schur-type symmetric polynomials. More recently in 2022, Matherne, Morales, and Selover proved that chromatic symmetric functions of indifference graphs of abelian Dyck paths are Lorentzian. In this thesis, we study the more general class of Lorentzian polynomials that is also invariant under the standard permutation action on variables. Throughout this work, we give exposition to the classical theory of symmetric polynomials and Lorentzian polynomials. Then we present several fundamental results on symmetric Lorentzian polynomials and highlight potential avenues for future research. / År 2020 bevisade Huh-Matherne-Mészáros-St.Dizier att normaliserade schur polynom är lorentziska och antog att andra symmetriska polynom av Schur-typ också är det. År 2022 bevisade Matherne-Morales-Selover att kromatiska symmetriska funktioner för indifferensgrafer av abeliska Dyck-paths är lorentziska. Motiverade av dessa resultat studerar vi den mer allmänna klassen av lorentziska polynom som också är invarianta under standardpermutationsverkan på variabler. I avhandlingen ger vi några grundläggande resultat om symmetriska lorentziska polynom och pekar på möjliga framtida riktningar.
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Conjugacy Class Sizes of the Symmetric and Alternating GroupsDickson, Cavan James 16 May 2014 (has links)
No description available.
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Second moment of the central values of the symmetric square L-functionsLam, Wing Chung 19 May 2015 (has links)
No description available.
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Bounds for Hecke Eigenforms and Their Allied L-functionsZhang, Qing 28 May 2015 (has links)
No description available.
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Ultraintense Laser-Driven Relativistic Hydrodynamics for Plane Symmetric SystemsTalamo, James M. 20 May 2015 (has links)
No description available.
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Bounding the Maximal Character Degree in terms of Smaller Degrees in the Symmetric GroupsSoomro, Sadaf Komal 13 September 2018 (has links)
No description available.
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Structure of Permutation PolynomialsDiene, Adama 30 September 2005 (has links)
No description available.
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Semi-Regular Sequences over F2Molina Aristizabal, Sergio D. January 2015 (has links)
No description available.
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Dynamical Systems in Cell Division Cycle, Winnerless Competition Models, and Tensor ApproximationsGong, Xue 08 July 2016 (has links)
No description available.
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