Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 16 of 16 for “"projective planes"”.
-
On Projective Planes & Rational Identities
… the presence of an underlying division ring in a projective plane. Supplementing this correspondence is the general theory of intersection theorems, which, restricted to desarguian projective planes P, corresponds precisely to the theory of integral rational identities, restricted to division …
-
On Nonassociative Division Rings and Projective Planes
… paper. Semifields have intimate ties to finite projective planes. In short, a finite projective plane with certain restrictions gives rise to a semifield, and, in turn, a finite semifield can be used via a coordinate construction, to build a special finite projective plane. It is also shown that …
-
Loops and Finite Affine Planes
The Prime Power Conjecture for Finite Projective Planes motivates the research that we present here. We establish a correspondence between finite affine planes and certain finite fibered loops. We prove that certain finite affine planes must have even prime power order. Finally, we characterize the …
-
Finite geometries and block designs
… in finite geometry, specifically affine and projective planes as well as block designs. We conclude with a chapter on how to apply these ideas to coding theory. Some of the results we look at include both the Bruck-Ryser and Bruck-Ryser-Chowla theorems as well as considering isomorphisms and …
-
An investigation of relationships between graph theory and coding theory
… designs, orthogonal latin squares and finite projective planes and various existence and non-existence results are derived for completely regular codes in three infinite families of distance-regular graphs.
-
Elliptic Curves Over Finite Fields
… over finite fields. In Chapter 1, affine and projective planes are introduced. Chapter 2 introduces the theory of algebraic curves and the Weierstrass Normal Form of a cubic curve is derived. In Chapter 3 we define derivations on arbitrary polynomial rings, and prove the group law for elliptic …
-
Homogeneous spaces with the cohomology of sphere products and compact quadrangles
… type. They are a far-reaching generalization of projective spaces, in particular a generalization of projective planes. There is another generalization of projective planes called generalized polygons. A projective plane is the same as a generalized triangle. The generalized polygons are also …
-
On Boolean functions, symmetric cryptography and algebraic coding theory
… of incidence structures such as 2-designs and projective planes. Then we consider the more general case when the side information are coded, the index coding with coded side information (ICCSI) problem. We extend some results on the error correction index codes to the ICCSI problem case and a …
-
Hyperovals, Laguerre planes and hemisystems - an approach via symmetry
… first look at hyperovals in finite Desarguesian projective planes. In the last 25 years a number of infinite families have been constructed. The area has seen a lot of activity, motivated by links with flocks, generalized quadrangles, and Laguerre planes, amongst others. An important element in …
-
A Method of Coordinatizing an Affine Geometry
… recent work, which dealt with coordinatizing projective planes, was primarily due to the mathematician, Marshall Hall, Jr. Although Hall's paper dealt with projective geometry, many mathematicians have since utilized his methods for coordinatizing the affine plane. Unlike the original analytic …
-
Three-dimensional manifolds
… are proved. The most important theorem is the Projective Plane Theorem (6.1), in which it is proved that elements of the second homotopy group of a 3-manifold can be represented, in a certain sense, by 2-spheres or projective planes in the manifold. The Projective Plane Theorem is, perhaps, an …
-
Nontraditional Positional Games: New methods and boards for playing Tic-Tac-Toe
… the traditional Tic-Tac-Toe board, on the finite planes <i>AG(2, q)</i> and <i>PG(2, q)</i> as well as on a new class of boards which we call nested boards. A nested board is created by replacing the points of one board with copies of a second board. We also consider the traditional positional …
-
Nontraditional Positional Games: New methods and boards for playing Tic-Tac-Toe
… the traditional Tic-Tac-Toe board, on the finite planes <i>AG(2, q)</i> and <i>PG(2, q)</i> as well as on a new class of boards which we call nested boards. A nested board is created by replacing the points of one board with copies of a second board. We also consider the traditional positional …
-
Conics, unitals and net replacement.
… unitals and conics in finite translation planes. Translation planes may be constructed from particular incidences in other translation planes. One method for doing this is "net-derivation" or the corresponding operation "net replacement". We consider conics and unitals of the finite …