Orientador: José Plínio de Oliveira Santos / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-25T04:32:08Z (GMT). No. of bitstreams: 1 BrasilJunior_NelsonGomes_M.pdf: 980636 bytes, checksum: dd8d61baeb633d5f598abc3523def800 (MD5) Previous issue date: 2014 / Resumo: Neste trabalho, estudamos a sequência dos Números de Catalan, uma sequência que aparece como solução de vários problemas de contagem envolvendo árvores, palavras, grafos e outras estruturas combinatórias. Atualmente, são conhecidas cerca de 200 interpretações combinatórias distintas para os Números de Catalan, o que motiva o estudo de relações entre estas interpretações, isto é, entre conjuntos cuja cardinalidade é dada pelos termos desta sequência. O principal objetivo do nosso trabalho é, portanto, mostrar bijeções entre esses conjuntos. No início do texto fazemos uma pequena introdução histórica aos números de Catalan, assim como definimos algumas formas de representar a sequência estudada. Depois mostramos algumas bijeções clássicas entre conjuntos contados pela sequência de Catalan. Além disso, apresentamos outras bijeções entre conjuntos envolvendo diversos objetos combinatórios. No total, são exibidas 29 bijeções / Abstract: In this work, we study the sequence of Catalan Numbers, which appears as a solution of many counting problems involving trees, words, graphs and other combinatorial structures. Nowadays, about 200 different combinatorial interpretations of the Catalan Numbers are known and that motivates the study between them, i. e., the study between sets whose cardinality is given by the terms of this sequence. The main objective of our work is therefore to show bijections between these sets. In the beginning, we make a short historical introduction of the Catalan Numbers and define some ways to represent the sequence. After that, we show some classical bijections between sets counted by the Catalan Numbers. Additionally, we exhibit other bijections between sets involving several combinatorial objects. Altogether, 29 bijections are presented / Mestrado / Matematica Aplicada / Mestre em Matemática Aplicada

Depuis quelques années, les gouvernements successifs et les organisations sportives nationales et internationales développent des politiques volontaristes en matière d'égalité et de parité dans le sport. Quel est l'effet réel de ces dispositifs, mesures et recommandations ? Menée conjointement dans le département des Pyrénées-Orientales (Languedoc-Roussillon) et au sein de la Communauté autonome de Gérone (Catalogne), notre étude s'intéresse à l'accès des femmes bénévoles aux postes à responsabilités dans le mouvement sportif local. Utilisant les résultats d'une enquête de terrain dans l’Espace Catalan Transfrontalier, cette thèse propose d'analyser la place et l'expérience des femmes dirigeantes dans les clubs de judo. La comparaison nous semble pertinente sur les plans scientifique et politique parce qu'elle nous permet de saisir les continuités culturelles à propos des rapports sexués dans le sport mais également les variations liés aux contextes nationaux et aux effets des politiques publiques. A partir de monographies de club de l'espace catalan choisis de part et d'autre de la frontière, nous tenterons de décrire les postes occupés, les parcours de dirigeantes mais également les freins à leur investissement bénévole. Il s'agira ainsi non seulement de comparer la manière dont ces femmes ont atteint leurs positions de « pouvoir » (carrières, vie de famille, capital sportif, fonctionnement des clubs...), mais également de saisir la manière dont elles perçoivent l'exercice de leurs fonctions. Dans une pratique de compétition fortement associée aux valeurs de virilité, comment des femmes arrivent à percer le « plafond de verre » ? Dans quelle mesure peut-on parler de domination masculine ? Peut-on distinguer des facteurs facilitateurs selon le pays d'origine ou, au contraire de freins identiques ?Cette thèse propose finalement de coupler l'analyse des rapports sociaux de sexe dans les clubs sportifs et celle de la comparaison pour mieux comprendre les effets respectifs des contextes politico-institutionnel sur le fait social étudié. / For the past few years, successive governments and national sports associations have developed a proactive policy as regards equality and parity in sports. What is the real impact of these schemes, actions and recommendations? Jointly carried out in the Pyrénées-Orientales (French region of Languedoc-Roussillon) and within the Autonomous Community of Gerone (Calalonia), our study concentrates on volunteer women’s access to positions of responsibility in local sports clubs. Using the results of a field study made in the Catalan cross-border area, this thesis provides a comprehensive assessment of the position and experience of women leaders in judo clubs. We consider that this comparison is relevant both on scientific and political levels since it allows to understand cultural continuities of gender relations in sports. Moreover, we will also consider the differences linked to the national background and to the consequences of public policies. From monographs of clubs chosen on both sides of the border, we will try and describe the positions and career paths of women managers, but also how their volunteer investment was sometimes held back. In this respect, not only we will compare how these women have reached their leading positions (career, family life, sport capital, clubs operation…) but also we will understand how they themselves consider their duties. Given a fierce competition strongly associated with the values of virility, how do women succeed in breaking the glass ceiling? Is it possible to distinguish between enabling factors or identical brakes, according to the country?Eventually, this thesis provides a combined analysis of gender social relations in sports clubs and a comparison to better understand the respective consequences of political and institutional contexts on the purpose of this study.

In the last few decades, combinatorial families exhibiting noncrossing or cluster phenomena have proven useful in understanding and connecting mathematical objects arising in seemingly unrelated branches of mathematics and theoretical physics. These phenomena can be modeled in the context of Coxeter groups and play an important role in algebraic combinatorics. In finite type, such families are enumerated by generalized Catalan numbers. In this thesis, we consider the extension of this theory to parabolic quotients of Coxeter groups. We outline the history, present the basic definitions and constructions, and provide a number of conjectures and research challenges arising in this context. We then solve these questions in linear type A and exhibit surprising connections of this theory to certain Hopf algebras and to the theory of diagonal harmonics. We end this thesis by proposing related directions for future research.:Chapter 0. Prologue Noncrossing partitions Triangulations Stack-sortable permutations Dyck paths Chapter 1. Preliminaries 1.1. Posets and lattices 1.1.1. A notion of order 1.1.2. Diagrams and labelings 1.1.3. Duality and multichains 1.1.4. Zeta polynomial and Möbius function 1.1.5. Lattices 1.1.6. Distributivity 1.1.7. Semidistributivity 1.1.8. Trimness 1.1.9. Congruence-uniformity 1.1.10. The core label order 1.2. Coxeter groups 1.2.1. Coxeter systems 1.2.2. The geometric representation 1.2.3. Ordering a Coxeter group 1.2.4. Orienting a Coxeter group Chapter 2. Cataland 2.1. Catalan numbers 2.2. Aligned elements 2.2.1. Cambrian lattices 2.3. Noncrossing partitions 2.4. Clusters 2.5. Nonnesting partitions 2.5.1. v-Tamari lattices 2.6. Chapoton Triangles Chapter 3. Parabolic Cataland: Origins 3.1. Parabolic quotients of Coxeter groups 3.2. Parabolic aligned elements 3.3. Parabolic noncrossing partitions 3.4. Parabolic clusters 3.5. Parabolic nonnesting partitions 3.6. Parabolic Chapoton triangles Chapter 4. Parabolic Cataland: Linear type A 4.1. Definitions 4.1.1. Parabolic quotients of the symmetric group 4.1.2. The longest α-permutation 4.1.3. The root poset of S_α and α-Dyck paths 4.1.4. c-clusters for S_α 4.1.5. c-aligned elements for S_α 4.1.6. c-noncrossing partitions for S_α 4.1.7. α-trees 4.2. Bijections 4.2.1. Noncrossing α-partitions and (α, 231)-avoiding permutations 4.2.2. Noncrossing α-partitions and α-Dyck paths 4.2.3. α-trees and (α, 231)-avoiding permutations 4.2.4. α-trees and noncrossing α-partitions 4.2.5. α-trees and α-Dyck paths 4.3. Posets 4.3.1. The weak order on S_α(231) 4.3.2. The rotation order on Dyck(α) 4.3.3. The core label order of Tam(α) 4.4. Chapoton triangles 4.5. Applications 4.5.1. A Hopf algebra on pipe dreams 4.5.2. A zeta map from diagonal harmonics Chapter 5. Epilogue 5.1. Arbitrary type A 5.2. Linear type B 5.3. (α, m)-Tamari lattices 5.4. Parabolic multiclusters Chapter A. Data A.1. Parabolic Catalan numbers in rank 3 A.2. Parabolic Catalan numbers in rank 4 A.3. Answers to Research Challenge 3.3.4 in rank 4 / Kombinatorische Familien, die nichtkreuzende oder Cluster-Phänomene aufweisen, haben sich in den letzten Jahrzehnten als wichtiges Werkzeug für das Verständnis und die Verbindung mathematischer Objekte aus scheinbar unverbundenen Teilgebieten der Mathematik und der theoretischen Physik erwiesen. Diese Phänomene können im Zusammenhang mit Coxeter-Gruppen modelliert werden, und spielen eine wichtige Rolle in der algebraischen Kombinatorik. Im endlichen Fall werden derartige kombinatorische Familien von verallgemeinerten Catalanzahlen abgezählt. In dieser Schrift betrachten wir eine Erweiterung dieser Theorie auf parabolische Quotienten von Coxeter-Gruppen. Wir stellen die historische Entwicklung und die grundlegenden Definitionen und Konstruktionen dar und präsentieren eine Reihe von Vermutungen und Forschungsfragen, die in diesem Zusammenhang entstehen. Anschließend lösen wir diese Fragen im sogenannten 'linearen Typ A' und decken überraschende Zusammenhänge dieser Theorie zu bestimmten Hopf-Algebren und zur Theorie der diagonal-harmonischen Polynome auf. Am Ende dieser Schrift schlagen wir weiterführende Forschungsrichtungen vor.:Chapter 0. Prologue Noncrossing partitions Triangulations Stack-sortable permutations Dyck paths Chapter 1. Preliminaries 1.1. Posets and lattices 1.1.1. A notion of order 1.1.2. Diagrams and labelings 1.1.3. Duality and multichains 1.1.4. Zeta polynomial and Möbius function 1.1.5. Lattices 1.1.6. Distributivity 1.1.7. Semidistributivity 1.1.8. Trimness 1.1.9. Congruence-uniformity 1.1.10. The core label order 1.2. Coxeter groups 1.2.1. Coxeter systems 1.2.2. The geometric representation 1.2.3. Ordering a Coxeter group 1.2.4. Orienting a Coxeter group Chapter 2. Cataland 2.1. Catalan numbers 2.2. Aligned elements 2.2.1. Cambrian lattices 2.3. Noncrossing partitions 2.4. Clusters 2.5. Nonnesting partitions 2.5.1. v-Tamari lattices 2.6. Chapoton Triangles Chapter 3. Parabolic Cataland: Origins 3.1. Parabolic quotients of Coxeter groups 3.2. Parabolic aligned elements 3.3. Parabolic noncrossing partitions 3.4. Parabolic clusters 3.5. Parabolic nonnesting partitions 3.6. Parabolic Chapoton triangles Chapter 4. Parabolic Cataland: Linear type A 4.1. Definitions 4.1.1. Parabolic quotients of the symmetric group 4.1.2. The longest α-permutation 4.1.3. The root poset of S_α and α-Dyck paths 4.1.4. c-clusters for S_α 4.1.5. c-aligned elements for S_α 4.1.6. c-noncrossing partitions for S_α 4.1.7. α-trees 4.2. Bijections 4.2.1. Noncrossing α-partitions and (α, 231)-avoiding permutations 4.2.2. Noncrossing α-partitions and α-Dyck paths 4.2.3. α-trees and (α, 231)-avoiding permutations 4.2.4. α-trees and noncrossing α-partitions 4.2.5. α-trees and α-Dyck paths 4.3. Posets 4.3.1. The weak order on S_α(231) 4.3.2. The rotation order on Dyck(α) 4.3.3. The core label order of Tam(α) 4.4. Chapoton triangles 4.5. Applications 4.5.1. A Hopf algebra on pipe dreams 4.5.2. A zeta map from diagonal harmonics Chapter 5. Epilogue 5.1. Arbitrary type A 5.2. Linear type B 5.3. (α, m)-Tamari lattices 5.4. Parabolic multiclusters Chapter A. Data A.1. Parabolic Catalan numbers in rank 3 A.2. Parabolic Catalan numbers in rank 4 A.3. Answers to Research Challenge 3.3.4 in rank 4

本篇文章是針對「凸多邊形的三角化」和「正方形街道中，好路徑的方法」(正方形街道中走 步 向右， 步 向上，且沿途中 不超過 的捷徑走法)兩者之間的對應關係的探討。

The aim of the thesis is to analyse the interjections in Spanish and Czech with regard to Catalan. The thesis consists of two parts - theoretical and practical. The theoretical one is focused on the definition of interjections form the grammatical point of view; moreover, it describes the distinction between proper and improper interjections. Subsequently, it goes through the role of interjections in the field of pragmatics, especially in terms of interpretation of the utterance and expression of its modal meanings. According to the predominant function, they are classified into mainly three categories - expressive, apellative and phatic. The practical part is focused on analysing some of the most important Spanish proper interjections: eh, ah, oh, ay, bah, uy, ja, zas, pum, hum and uf and their Catalan equivalent eh, ah, oh, ai, bah, ui, ha ha, zas (or xac), pum, hum and uf. The analysis is based on the linguistic corpus InterCorp. The most important part of the practical part are Spanish interjections and their Czech equivalents, while the Catalan ones are considered complementary. Key words: interjections - Spanish - Czech - Catalan - modality - pragmatics - linguistic corpus

Le travail repose sur un constat selon lequel le terme « immigré » est présent dans le discours politique et intellectuel catalan depuis le début du XXe siècle pour désigner les Espagnols venus vivre en Catalogne. L’appellation choisie pour désigner les migrants venus d’autres régions d’Espagne est en contradiction avec sa définition qui sous-entend un dépassement de frontière étatique. La distinction du lieu d’origine permet d’en désigner une autre : celle de l’identité. Une différence est créée et entretenue entre deux groupes vivant sur un même territoire et partageant une même nationalité espagnole, mais dont le lieu de naissance est à l’intérieur ou à l’extérieur de la Catalogne. En développant une image de l’« immigré », le discours catalan insiste sur le fait que ce flux de population provienne d’un extérieur. S’exprimer sur ce sujet permet d’affirmer sa propre vision de la société catalane, comprise comme multiculturelle, biculturelle ou comme une unique communauté. Le point commun entre ces différentes manières de concevoir la catalanité réside dans l’affirmation de la cohérence et l’autonomie du groupe récepteur capable d’accueillir les autres, malgré les craintes de certains. Réfléchir sur le phénomène migratoire permet finalement au discours d’affirmer sa propre identité et l’existence d’une nation catalane. L’« immigré » a également un rôle dans ce processus en participant à l’évolution de sa propre image discursive ou à travers les premières générations nées en Catalogne. Son image est bien au centre de luttes de classements et apparaît comme un instrument permettant d’imposer une idéologie nationale ou une manière de concevoir la société catalane. / This work builds up on the fact that the word « immigrant » is present on the political and intellectual Catalan discourse since the beginning of the XXth century to reference Spaniards coming to live in Catalonia. The appellation chosen by this discourse to name immigrants coming from other regions of Spain is openly contradictory with its definition that imply crossing a national frontier. The distinction regarding place of origin allows for another one: Identity. This difference is created and sustained by these two groups living under the same territory and sharing the Spanish nationality, but whose place of birth is inside or outside Catalonia. Developing an image of the « immigrant », the catalan discourse insists on the fact that this flow of people come from an outside. Expressing oneself over this subject allows for an original vision of the Catalan society, understood as multicultural, bicultural or as a unique community. The common point between these different ways of conceiving catalanity resides on the affirmation of the receptor group ´s coherence and autonomy and its capacity to host others. Thinking about the immigration phenomenon enables the discourse to affirm its own identity and the existence of a catalan nation. The « immigrant » also plays a role in this process participating in the evolution of its own discourse image or through the first generations born in catalonia. Their image is immerse in between the classification struggles and appears as an instrument that allows for an imposition of a national ideology or a way of conceiving the catalan.

Made available in DSpace on 2016-04-27T19:30:32Z (GMT). No. of bitstreams: 1 Fernanda Rorigues Galve.pdf: 920021 bytes, checksum: 7128fc7dae8c7d7e70c4fa0aa97ec0b6 (MD5) Previous issue date: 2012-05-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This thesis is a navigation in the multiplicity of João Cabral de Melo Neto´s life and work. The anchorage of the research is in the visibility of the poetic work with the approach of its meanings and mediations in the sea of History. It attempts to reflect how the ability of artistic praxis holds itself a political and historical dimension. The thesis presents the story of a man that when experiences the literature´s fascinations and challenges, adds them to the reflexion in his dialog with several societies and friends. We have an anthology of great moments of the author (either as a diplomat, critic, historian, printer and man of words). A true nautical letter on art, literaly creation, societies, politics and, of course, life. This thesis elapses the life of a man who records and "dwells time" and learns which is lived in poetic words / Esta tese é uma navegação no multiverso da vida e obra de João Cabral de Melo Neto, cujo ancoramento está na visibilidade do trabalho poético com a aproximação de seus significados e mediações no mar da história. Busca-se refletir como a capacidade da práxis artística comportar em si uma dimensão política e histórica. A tese apresenta a história de um homem que, ao experimentar os fascínios e os desafios da literatura, soma-as à reflexão em seu diálogo com várias sociedades e amigos. Temos uma antologia de grandes momentos do autor (seja como diplomata, crítico, historiador, impressor e homem da palavra). Uma verdadeira carta náutica sobre arte, criação literária, sociedades, política e, claro, a vida. Esta tese transcorre a vida de um homem que registra e habita o tempo e apreende o que é vivido em palavras poéticas

Dentre os meios utilizados para enriquecer os quadros dos paradigmas das flexões verbais nas línguas românicas, destaca-se o emprego de construções de caráter vulgar: as perífrases. Essas formas verbais compostas apresentam, por vezes, divergências relevantes entre as línguas românicas, como a construção ir (presente de indicativo) + infinitivo. Enquanto a língua portuguesa emprega essa perífrase para denotar noção de futuro, a língua catalã, ao contrário, utiliza-a para fazer referência a uma ação pretérita. Tendo em conta as demais línguas românicas, pode-se averiguar que é o catalão que faz uma exceção ao uso de ir+ infinitivo. Apesar de ter seu uso proliferado, o emprego da perífrase catalã não é consenso entre as suas variantes dialetais: enquanto a maior parte privilegia o uso da perífrase, em detrimento da forma simples de pretérito, uma pequena parte dá maior ênfase à forma sintética ou mescla as variantes. Ainda que a questão da coincidência formal da perífrase conduz a uma importante estranheza semântica em relação a outras línguas românicas, o escopo da pesquisa se mantém na comparação entre a língua portuguesa e catalã, colocando em xeque a relação dicotômica norma/ uso. Uma análise sob a perspectiva diacrônica poderia apresentar respostas satisfatórias para se chegar ao entendimento do tratamento e da história dessas perífrases nas duas línguas. / Among the means used to broaden the paradigm of verbal inflections in romance languages, the employment of constructions that are vulgar in character is noteworthy: the periphrases. The compound verb forms present, at times, significant differences between the romance languages, such as the construction ir (indicative present tense) + infinitive. Whereas in Portuguese such a pattern is employed to denote future, Catalan uses it to refer to past actions. All romance languages considered, it can be verified that Catalan is the only language that makes this exceptional use of ir + infinitive. In spite of its widespread use, the employment of the Catalan periphrasis is not a consensus amongst its dialects: while the majority of them make use of the periphrasis instead of the simple past form, a small part of them prefer to use the synthetic form or both interchangeably. Although the matter of the formal coincidence of the periphrasis leads to important semantic awkwardness in relation to the other romance languages, the scope of this work is the comparison between Portuguese and Catalan languages, calling into question the norm/usage dichotomy. An analysis in diachronic perspective could lead to satisfactory understanding of the treatment and history of these periphrases in both languages.

This study investigated language attitudes toward Valencian Catalan and Castilian among university affiliates in Castellón de la Plana, Spain. One hundred informants completed an online survey regarding attitudes toward and uses of Valencian and Castilian in various situations. The results were first analyzed globally, then again based on the independent variables of age, sex, and mother tongue. The findings suggest that overall, informants held positive attitudes toward Valencian and Castilian and believed that it was important that the local language be preserved and passed down to the next generation. University-aged participants, those whose first language was either Valencian or both Valencian and Castilian, and females tended to hold slightly more positive attitudes toward Valencian than other groups.

Entablar contacto con un aspecto humano, con la razón interpuesta siquiera como afán, es una tarea que se convierte muy pronto en apasionante, mientras aquel aspecto crece su tamaño a mucha mayor velocidad que nuestro impulso: el plan inicial de trabajo, materializado en un programa de cinco hojas, abarcaba todos los niveles fonéticos que una bibliografía me sugirió sobre mi lengua materna. Quise decirlo todo; desde el dato minúsculo de un rasgo redundante hasta la frase enterna como emisión fónica en sus posibles perspectivas, pasando por la sílaba, fonética y estadísticamente estudiada. Vivir este problema –ese contacto entablado– hizo evolucionar en seguida las intención por etapas. Ahora, a poco más de un año de distancia, la parte descriptiva se ha concentrado definitivamente sobre el timbre vocálico, en un programa impsoible de esbozar en menos de seis hojas. A veces, aunque parezca mentira, detrás de un pequeño factor minuciosamente aprisionado se esconde una grandiosidad tan digna de ser contemplada como al fenómeno total del lenguaje en el primer atisbo de la consciencia. La parte general, por su lado, continúa preludiando como al princpio la labor de conjunto que, más pronto que tarde, será consumada. El presente estudio ha sido dividido en dos Partes: General (A) y Descriptiva (B). La primera de ellas consta de cinco Capítulos, que contienen sucesivamente el Objetivo y fines de esta tesis (I), el detalle de los Materiales utilizados (II), los Medios de Investigación aplicados (III), un apartado sobre Generalidades y Metodología (IV) y un último capítulo (V), con las formas de aplicación lingüística (V). Por su parte, la Parte Descriptiva incluye dos Capítulos: uno sobre el timbre vocálico (I) y otro recogiendo las conclusiones generales (II). Una bibliografía y dos índices (el primero de figuras y el segundo de materias) completan el articulado de la tesis.