|
|
Sudé triangulace a Abelovy grupy
Hrbek, Michal ; Drápal, Aleš (advisor) ; Kepka, Tomáš (referee)
Title: Even triangulations and Abelian groups Author: Michal Hrbek Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal CSc., DSc. Abstract: This thesis takes interest in spherical Eulerian triangulations and the algebraic structure defined on its vertices corresponding with the latin bitrade equivalent to the triangulation. First, we introduce needed results about the properties of the triangulations and their embeddings into Abelian groups. Then we get concerned with a particular kind of almost 6-homogenous triangulations. The text presents several examples, then the groups of the simplest sequence of triangulations are explicitly described. In order to investigate more complicated cases, we introduce a recursive formula for defining relations of the groups and we show an example of its usage with modular arithmetic. The thesis is completed by discussing computed data. Keywords: latin bitrade, eulerian triangulation, Abelian group 1
|
|
|
Sudé triangulace a Abelovy grupy
Hrbek, Michal ; Drápal, Aleš (advisor) ; Kepka, Tomáš (referee)
Title: Even triangulations and Abelian groups Author: Michal Hrbek Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal CSc., DSc. Abstract: This thesis takes interest in spherical Eulerian triangulations and the algebraic structure defined on its vertices corresponding with the latin bitrade equivalent to the triangulation. First, we introduce needed results about the properties of the triangulations and their embeddings into Abelian groups. Then we get concerned with a particular kind of almost 6-homogenous triangulations. The text presents several examples, then the groups of the simplest sequence of triangulations are explicitly described. In order to investigate more complicated cases, we introduce a recursive formula for defining relations of the groups and we show an example of its usage with modular arithmetic. The thesis is completed by discussing computed data. Keywords: latin bitrade, eulerian triangulation, Abelian group 1
|
|
|
Even triangulations and commutative groups
Luber, Jan ; Drápal, Aleš (advisor) ; Kepka, Tomáš (referee)
Title: Even triangulations and commutative groups Author: Jan Luber Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc. Abstract: This thesis takes interest in latin bitrades and triangulations construc- ted from them. Firstly, we introduce needed definitions, properties of the latin bitrades, detailed construction of the triangulation and mainly possibility of em- bedding latin bitrades into abelian groups. These groups are determined by the relations definied on vertices of the triangulation. Then we get concerned with a particular kind of 3-homogeneous latin bitrades which correspond to toroidal tri- angulation whose each vertex has degree six. For these groups we express relation matrix and complement to their torsion ranks. In case of simple triangulations we present explicit description of the groups and with modular arithmetic we get partial description even for more complex triangulations. Keywords: latin bitrade, eulerian triangulation, abelian group
|
guest ::
