Codis Z2Z4-additius en Magma

En aquest projecte es presenta el desenvolupament d'un paquet d'aplicacions en l'entorn de programació matemàtica Magma, per al tractament dels codis anomenats Z2Z4-additius. Els codis Z2Z4-additius permeten representar alguns codis binaris, com a codis lineals en l'espai dels codis Z2Z4-additius. Aquest fet permetrà l'estudi de tota una sèrie de codis binaris no lineals que fins ara eren intractables.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

Conjugacy of piecewise linear Lorenz map that expand on average

For piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a ß-transformation.