Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Classification of skew-symmetric forms corresponding to cluster algebras with principal coefficients
Download
index.pdf
Date
2016
Author
Mazı, Sedanur
Metadata
Show full item record
Item Usage Stats
205
views
106
downloads
Cite This
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.
Subject Keywords
Algebra.
,
Skew fields.
,
Cluster algebras.
URI
http://etd.lib.metu.edu.tr/upload/12620621/index.pdf
https://hdl.handle.net/11511/26167
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
On the arithmetic operations over finite fields of characteristic three with low complexity
AKLEYLEK, SEDAT; Özbudak, Ferruh; Özel, Claire Susanna (2014-03-15)
In this paper, the Hermite polynomial representation is adapted as a new way to represent certain finite fields of characteristic three. We give the multiplication method to multiply two elements of F-3n in the Hermite polynomial representation with subquadratic computational complexity by using a divide-and-conquer idea. We show that in some cases there is a set of irreducible binomials in the Hermite polynomial representation to obtain modular reduction with a lower addition complexity than the standard p...
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...
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...
Additive polynomials and primitive roots over finite fields
Özbudak, Ferruh (2001-01-01)
We prove existence of primitive roots with a prescribed nonzero image using the arithmetic of algebraic function fields for a class of polynomials over sufficiently large finite fields.
On multiplication in finite fields
Cenk, Murat; Özbudak, Ferruh (2010-04-01)
We present a method for multiplication in finite fields which gives multiplication algorithms with improved or best known bilinear complexities for certain finite fields. Our method generalizes some earlier methods and combines them with the recently introduced complexity notion (M) over cap (q)(l), which denotes the minimum number of multiplications needed in F-q in order to obtain the coefficients of the product of two arbitrary l-term polynomials modulo x(l) in F-q[x]. We study our method for the finite ...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
S. Mazı, “Classification of skew-symmetric forms corresponding to cluster algebras with principal coefficients,” M.S. - Master of Science, Middle East Technical University, 2016.