Now showing items 1-20 of 26

• #### A connection between Inverse Problems and Nonstandard Analysis ﻿

(Universitat Politècnica de Catalunya, 2018-10)
Master thesis
Restricted access - author's decision
Nonstandard analysis was born in the decade of 1960 an attempt to give a formal context to the Leibniz approach to differential calculus, in particular in order to provide a rigorous foundation to the notions of infinitesimal ...
• #### Additive structures and randomness in combinatorics ﻿

(Universitat Politècnica de Catalunya, 2020-07-03)
Doctoral thesis
Open Access
Arithmetic Combinatorics, Combinatorial Number Theory, Structural Additive Theory and Additive Number Theory are just some of the terms used to describe the vast field that sits at the intersection of Number Theory and ...
• #### An algebraic fractal approach to Collatz Conjecture ﻿

(Universitat Politècnica de Catalunya, 2019-05)
Bachelor thesis
Open Access
The Collatz conjecture is one of the most easy-to-state unsolved problems in Mathematics today. It states that after a finite number of iterations of the Collatz function, defined by C(n) = n/2 if n is even, and by C(n) = ...
• #### Brownian motion: a random walk approximation ﻿

(Universitat Politècnica de Catalunya, 2018-07)
Bachelor thesis
Open Access
Brownian motion is one of the most used stochastic models in applications to financial mathematics, communications, engineeering, physics and other areas. Many of the central results in the theory are obtained directly ...
• #### Characterizing universal intervals in the homomorphism order of digraphs ﻿

(Universitat Politècnica de Catalunya, 2020-07)
Master thesis
Open Access
In this thesis we characterize all intervals in the homomorphism order of digraphs in terms of universality. To do this, we first show that every interval of the class of digraphs containing cycles is universal. Then we ...
• #### Classical and modern approaches for Plünnecke-type inequalities ﻿

(Universitat Politècnica de Catalunya, 2015-09)
Bachelor thesis
Open Access
The main objective of this thesis is to present and prove Plünnecke's Inequality, a theorem that gives bounds for sumsets in commutative groups. An introduction to the theory of set addition is presented. Three different ...
• #### Colored combinatorial structures: homomorphisms and counting ﻿

(Universitat Politècnica de Catalunya, 2009-06-09)
Doctoral thesis
Open Access
A partir del problema de los cuatro colores se inicia el estudio de coloraciones en grafos; teoría que ha existido ya por más de 150 años, y se ocupa del problema fundamental de partir un conjunto en clases de acuerdo con ...
• #### Entropy methods for sumset inequalities ﻿

(Universitat Politècnica de Catalunya, 2016-07)
Master thesis
Open Access
In this thesis we present several analogies betweeen sumset inequalities and entropy inequalities. We offer an overview of the different results and techniques that have been developed during the last ten years, starting ...
• #### Markov chains and applications in the generation of combinatorial designs ﻿

(Universitat Politècnica de Catalunya / Universitat de Barcelona, 2018-01)
Master thesis
Open Access
This Thesis deals with discrete Markov chains and their applications in the generation of combinatorial designs. A conjecture on the generation of proper edge colorings of the complete graph K_n, for n even, is tackled. A ...
• #### Ohba’s conjecture and beyond for generalized colorings ﻿

(Universitat Politècnica de Catalunya, 2017-07)
Master thesis
Open Access
Let $G$ be a graph. Ohba's conjecture states that if $|V(G)|\leq 2\chi(G) +1$, then $\chi(G)=\chi^L(G)$. Noel, West, Wu and Zhu extended this result and proved that for any graph, \$\chi^L(G)\leq\max\{\chi(G),\left\lceil( ...
• #### Partition functions for states models on signed graphs ﻿

(Universitat Politècnica de Catalunya, 2020-02-25)
Bachelor thesis
Open Access
Covenantee:   Univerzita Karlova / Univerzita Karlova
There are many models of physical systems based in unsigned graph theory, however there are some systems that cannot be modelled by unsigned graphs and that is the reason of signed graph states models. For these models, ...
• #### Probabilistic methods and coloring problems in graphs ﻿

(Universitat Politècnica de Catalunya, 2010-06)
Master thesis
Open Access
Aquest projecte està dedicat a estudiar el k-èssim nombre cromàtic generalitzat que sorgeix de les descomposicions Low Tree--Depth en grafs usant mètodes probabilístics.. Una extensió natural del nombre cromàtic d'un graf ...
• #### Rainbow matchings in hypergraphs ﻿

(Universitat Politècnica de Catalunya, 2015-10)
Master thesis
Open Access
A rainbow matching in an edge colored multihypergraph is a matching consisting of edges with pairwise distinct colors. In this master thesis we give an overview of the results about having a rainbow matching in edge-colored ...
• #### Random combinatorial structures with low dependencies : existence and enumeration ﻿

(Universitat Politècnica de Catalunya, 2013-10-01)
Doctoral thesis
Open Access
En aquesta tesi s'estudien diferents problemes en el camp de la combinatòria i la teoria de grafs, utilitzant el mètode probabilístic. Aquesta tècnica, introduïda per Erdős , ha esdevingut una eina molt potent per tal de ...
• #### RECUBRIMIENTOS K-ARCO TRANSITIVOS DE DIGRAFOS ﻿

(Universitat Politècnica de Catalunya, 2001-02-02)
Doctoral thesis
Open Access
Un digrafo o grafo dirigido se dice que es k-arco transitivo si tiene grupo de automorfismos que actúa transitivamente en el conjunto de k-arcos. Para un entero positivo k, un k-arco de un digrafo es una secuencia ...
• #### Relació entre el grup de Thompson i el teorema dels quatre colors ﻿

(Universitat Politècnica de Catalunya, 2011)
Master thesis
Open Access
L'objectiu d'aquest treball és estudiar la relació que hi ha entre el Teorema dels Quatre Colors i els grups de Thompson. Principalment, es construeix el procés que permet passar d'un mapa a un (o més) elements del grup ...
• #### Removal lemmas in sparse graphs ﻿

(Universitat Politècnica de Catalunya, 2015-07)
Bachelor thesis
Open Access
In this work we explain and prove the graph removal lemma, both in its dense and sparse cases, and show how these can be applied to finite groups to obtain arithmetic removal lemmas. We show how the concept of regularity ...
• #### Shannon capacity and the Lovász Theta function ﻿

(Universitat Politècnica de Catalunya, 2019-05)
Bachelor thesis
Open Access
This thesis focuses on the study of two graph parameters known as the Shannon capacity and the Lovász number. The first was introduced by Claude Elwood Shannon on \cite{shannon} and describes the maximum rate at which ...
• #### Structure of sets with small sumset and applications ﻿

(Universitat Politècnica de Catalunya, 2008-10)
Master thesis
Open Access
It was the main objective of this master thesis to determine the position of the holes for sets with small doubling. The answer to this question was given recently by Freiman and in here we generalize it to the case with ...
• #### Study of balance and symmetry of rooted trees ﻿

(Universitat Politècnica de Catalunya, 2020-10)
Master thesis
Open Access
The Sacking index of a tree is a measure of balance which has beenintroduced in applications to phylogenetics. The study of this parameterin rooted binary trees, identifying its extremal values and enumerationof trees with ...