Essays about: "symmetric polynomials"

Showing result 1 - 5 of 6 essays containing the words symmetric polynomials.

  1. 1. Symmetric Lorentzian polynomials

    University essay from KTH/Matematik (Avd.)

    Author : Daniel Qin; [2023]
    Keywords : symmetric polynomials; Lorentzian polynomials; matroids; symmetriska polynom; lorentziska polynom; matroid;

    Abstract : 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. READ MORE

  3. 2. Asymptotics of beta-Hermite Ensembles

    University essay from Linköpings universitet/Matematisk statistik; Linköpings universitet/Tekniska fakulteten

    Author : Filip Berglund; [2020]
    Keywords : beta-Hermite ensembles; Gaussian ensembles; empirical distribution function; level density; largest eigenvalue; order statistic; Sturm sequence; Hermite polynomials; beta-Hermite ensemblerna; gaussiska ensemblerna; empiriska fördelningsfunktionen; nivåtäthet; största egenvärdet; ordningsstatiska; Sturmföljder; Hermitepolynom;

    Abstract : In this thesis we present results about some eigenvalue statistics of the beta-Hermite ensembles, both in the classical cases corresponding to beta = 1, 2, 4, that is the Gaussian orthogonal ensemble (consisting of real symmetric matrices), the Gaussian unitary ensemble (consisting of complex Hermitian matrices) and the Gaussian symplectic ensembles (consisting of quaternionic self-dual matrices) respectively. We also look at the less explored general beta-Hermite ensembles (consisting of real tridiagonal symmetric matrices). READ MORE

  4. 3. Perturbations of symmetricmatrix polynomials and theirlinearization

    University essay from Örebro universitet/Institutionen för naturvetenskap och teknik

    Author : Edgar Skönnegård; [2020]
    Keywords : ;

    Abstract : The canonical stucture information, i.e. the elementary divisors and minimalindices of a matrix polynomial, is sensitive to perturbations of the matrixcoefficients of the polynomial, e.g. READ MORE

  5. 4. Combinatorics of Macdonald polynomials and cyclic sieving

    University essay from KTH/Matematik (Avd.)

    Author : Joakim Uhlin; [2019]
    Keywords : ;

    Abstract : In this thesis, we study the non-symmetric Macdonald polynomials E_λ (x;q,t) at t=0 from a combinatorial point of view, using the combinatorial formula found by J. Haglund, M. Haiman, and N. Loehr. READ MORE

  6. 5. Alternative Polynomials for Rijndael : Diffusion Analysis

    University essay from Linnéuniversitetet/Institutionen för datavetenskap (DV)

    Author : Hamid Noroozi; [2014]
    Keywords : Rijndael; Advanced Encryption Standard; Symmetric key Encryption; Diffusion Analysis; Mathematica; Irreducible Polynomial;

    Abstract : The Rijndael cryptosystem uses a particular polynomial to create its constants. All calculations within the encryption and decryption layers are based on this polynomial. This arouse the curiosity to see what happens if the polynomial is substituted by other polynomials. READ MORE