Some New Bounds on Closed Ordinal Ramsey Numbers

Sağlam, Irmak
Partition calculus on ordinals was introduced by Erd ̋os and Rado and is a well-studiedsubject. Later on, Baumgartner extended this investigation to topological spaces andstudied topological partition relations on ordinal spaces.In recent years, closed and topological partition relations on ordinals have been anactive area of research. This thesis is a contribution to the study of closed ordinalRamsey numbers. More specifically, we provide new lower and upper bounds forclosed ordinal Ramsey numbers of pairs of small countable ordinals. These boundsimprove the previously known bounds given by Caicedo and Hilton.


Some maximal function fields and additive polynomials
GARCİA, Arnaldo; Özbudak, Ferruh (Informa UK Limited, 2007-01-01)
We derive explicit equations for the maximal function fields F over F-q(2n) given by F = F-q(2n) (X, Y) with the relation A(Y) = f(X), where A(Y) and f(X) are polynomials with coefficients in the finite field F-q(2n), and where A(Y) is q- additive and deg(f) = q(n) + 1. We prove in particular that such maximal function fields F are Galois subfields of the Hermitian function field H over F-q(2n) (i.e., the extension H/F is Galois).
Galois structure of modular forms of even weight
Gurel, E. (Elsevier BV, 2009-10-01)
We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
Value sets of Lattes maps over finite fields
Küçüksakallı, Ömer (Elsevier BV, 2014-10-01)
We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication.
Improved p-ary codes and sequence families from Galois rings
Ling, San; Özbudak, Ferruh (2005-01-01)
In this paper, a recent bound on some Weil-type exponential sums over Galois rings is used in the construction of codes and sequences. The bound on these type of exponential sums provides a lower bound for the minimum distance of a family of codes over F-p, mostly nonlinear, of length p(m+1) and size p(2) (.) p(m)((D-[D/p2])), where 1 <= D <= p(m/2). Several families of pairwise cyclically distinct p-ary sequences of period p(p(m) - 1) of low correlation are also constructed. They compare favorably with cer...
Khrebtova, Ekaterina S.; Malinin, Dmitry (World Scientific Pub Co Pte Lt, 2008-12-01)
We prove the existence and finiteness theorems for integral representations stable under Galois operation. An explicit construction of the realization fields for representations of finite groups stable under the natural operation of the Galois group is given. We also compare the representations over fields and the rings of integers, and give a quantitative result on the rarity of integral Galois stable representations. There is a series of related conjectures and applications to arithmetic algebraic geometr...
Citation Formats
I. Sağlam, “Some New Bounds on Closed Ordinal Ramsey Numbers,” M.S. - Master of Science, Middle East Technical University, 2020.