Classification of skew-symmetric forms corresponding to cluster algebras with principal coefficients

Mazı, Sedanur
In this thesis, we study algebraic and combinatorial properties of the skew-symmetric forms that correspond to cluster algebras with principal coefficients. We obtain a classification of these forms under congruence and compute the Arf invariants for finite types. 


Seven, Ahmet İrfan (2013-05-01)
Mutation of skew-symmetrizable matrices is a fundamental operation that first arose in Fomin-Zelevinsky's theory of cluster algebras; it also appears naturally in many different areas of mathematics. In this paper, we study mutation classes of skew-symmetrizable 3 x 3 matrices and associated graphs. We determine representatives for these classes using a natural minimality condition, generalizing and strengthening results of Beineke-BrustleHille and Felikson-Shapiro-Tumarkin. Furthermore, we obtain a new num...
Quasi-Cartan companions of elliptic cluster algebras
Velioğlu, Kutlucan; Seven, Ahmet İrfan; Department of Mathematics (2016)
There is an analogy between combinatorial aspects of cluster algebras and diagrams corresponding to skew-symmetrizable matrices. In this thesis, we study quasi-Cartan companions of skew-symmetric matrices in the mutation-class of exceptional elliptic diagrams. In particular, we establish the existence of semipositive admissible quasi-Cartan companions for these matrices and exhibit some other invariant properties.
A New Representation of Elements of Binary Fields with Subquadratic Space Complexity Multiplication of Polynomials
Özbudak, Ferruh; Cenk, Murat (2013-10-01)
In this paper, Hermite polynomial representation is proposed as an alternative way to represent finite fields of characteristic two. We show that multiplication in Hermite polynomial representation can be achieved with subquadratic space complexity. This representation enables us to find binomial or trinomial irreducible polynomials which allows us faster modular reduction over binary fields when there is no desirable such low weight irreducible polynomial in other representations. We then show that the pro...
Calculations of the roots of classical orthogonal polynomials: an application to gaussian quadrature
Shaidolda, Gulnaz; Taşeli, Hasan; Department of Mathematics (2019)
This thesis focuses on classical orthogonal polynomials namely Jacobi, Laguerre and Hermite polynomials and a method to calculate the roots of these polynomials is constructed. The roots are expressed as the eigenvalues of a tridiagonal matrix whose coefficients depend on the recurrence formula for the classical orthogonal polynomials. These approximations of roots are used as method of computation of Gaussian quadratures. Then the discussion of the numerical results are then introduced to deduce the effici...
Characterisation and enumeration of a class of semi bent quadratic Boolean functions
KOÇAK, Neşe; Koçak, Onur Ozan; Özbudak, Ferruh; SAYGI, ZÜLFÜKAR (2015-01-01)
In this paper, we consider semi-bentness of quadratic Boolean functions defined for even n and give the characterisation of these functions. Up to our knowledge, semi-bentness of this class has not been investigated before and we proved that semi-bent functions of this form exist only for 6|n. Furthermore, we present a method for enumeration of semi-bent and bent functions in certain classes. Using this method we find the exact number of semi-bent functions of this form. Moreover, we complete some previous ...
Citation Formats
S. Mazı, “Classification of skew-symmetric forms corresponding to cluster algebras with principal coefficients,” M.S. - Master of Science, Middle East Technical University, 2016.