Books by Rodrigo De Castro Korgi
This volume in the Texts in Logic and Games series grew out of the seventh conference on Logic an... more This volume in the Texts in Logic and Games series grew out of the seventh conference on Logic and the Founda tions of the Theory of Games and Decisions (LOFT 7), which took place in Liverpool, in July 2006. The LOFT conferences are interdisciplinary events that bring together researchers from a variety of fields: compu ter science, economics, game theory, linguistics, logic, multiagent systems, psychology, philosophy, social choice and statistics. Topics that fall under the LOFT umbrella include epistemic and temporal logic, theories of information processing and belief revision, models of bounded rationality, nonmonotonic reasoning, theories of learning and evolution, mental models, etc. The papers collected in this volume reflect the variety of interests and the interdisciplinary composition of the LOFT com munity. 9 7 8 9 0 8 9 6 4 0 2 6 0 isbn 978 90 8964 026 0 amsTerdam universiTy press www.aup.nL amstErdam univErsity prEss
Papers by Rodrigo De Castro Korgi
en las teorías U2 (i ~ 1) de aritmética acotada de segundo orden introducidas por S. Buss. En par... more en las teorías U2 (i ~ 1) de aritmética acotada de segundo orden introducidas por S. Buss. En particular, se demuestra que la clase de las funciones ¿;:,b_ definibles en Uz es cerrada bajo recursión acotada, o, equivalentemente, que U:í puede ¿;~,b-definir [2, la segunda clase Grzegorczyk. Abstract. Jt is shown that some recursion schemes can be carried out in the secotul order theories of Bounded Arithmetic Uz (i ~ 1) introduced by S. Buss in f2}. In particular, we pro ve that the class of ¿;i,b-definable functions in Uz is closed under bounded recursion, or, equivalently, that U ~ can ¿;;,b-define the functions in the second class of Grzegorczyk, [2.
En esta nota re-examinamos una importante y bella construccion matematica: el llamado completamie... more En esta nota re-examinamos una importante y bella construccion matematica: el llamado completamiento de Dedekind-MacNeille, DM(P), de un conjunto ordenado (P,≤). Dicho completamiento, tambien conocido como completamiento normal de P, fue originalmente propuesto por H. M. MacNeille en 1937 [8] como una generalizacion de la famosa construccion de los numeros reales a partir de los racionales publicada por R. Dedekind 65 anos antes, en 1872 [4].
In sheaf theory we have at our disposal the so called "germination process" by means of... more In sheaf theory we have at our disposal the so called "germination process" by means of which a sheaf can be obtained, in a natural manner, from data provided by a presheaf. Essentially, "germination" is a stalk producing mechanism that requires direct systems, whose colimits are the desired stalks of the sheaf.
El libro esta escrito tanto para estudiantes de matematicas -quienes, es de suponer, tienen mas e... more El libro esta escrito tanto para estudiantes de matematicas -quienes, es de suponer, tienen mas experiencia con razonamientos abstractos y demostraciones- como para estudiantes de ingenieria. Es el profesor quien debe establecer el tono del curso, enfatizando ya sea el rigor matematico o una presentacion mas intuitiva y practica. Los resultados estan presentados en forma de teoremas, corolarios y lemas, con sus respectivas demostraciones; estas pueden omitirse, si asi lo estima el profesor. En los cursos dirigidos a estudiantes de ingenieria de sistemas, el enfasis debe residir -tanto por parte del profesor como por parte del estudiante--- en los ejemplos y ejercicios practicos; hay que resaltar mas el significado de los enunciados que sus demostraciones formales. El libro contiene gran cantidad de ejemplos y problemas resueltos, con aplicaciones o ilustraciones directas de la teoria. Como prerrequisito, es imprescindible que el estudiante haya tomado al menos un curso de matematica...
The Mathematical Intelligencer
In this paper, we introduce a new family of generalized colored Motzkin paths, where horizontal s... more In this paper, we introduce a new family of generalized colored Motzkin paths, where horizontal steps are colored by means of $F_{k,l}$ colors, where $F_{k,l}$ is the $l$th $k$-Fibonacci number. We study the enumeration of this family according to the length. For this, we use infinite weighted automata.
The Mathematical Intelligencer, 1999
ar-Rous rails to Paul Erdds ~ he notion of Erdds number has floated around the mathematical resea... more ar-Rous rails to Paul Erdds ~ he notion of Erdds number has floated around the mathematical research community for more than thirty years, as a way to quantify the common knowledge that mathematical and scientific research has become a very collaborative process in the twentieth century, not an activity engaged in solely by isolated individuals. In this paper we explore some (fairly short) collaboration paths that one can follow from Paul Erd6s to researchers inside and outside of mathematics.
accefyn.org.co
Page 1. Historia di: i.л Ciencia TODOS LOS CAMINOS CONDUCEN A PAUL ERDÒS* por Rodrigo De Castro1,... more Page 1. Historia di: i.л Ciencia TODOS LOS CAMINOS CONDUCEN A PAUL ERDÒS* por Rodrigo De Castro1, Jerrold W. Grossman1 Resumen R. D Castro & JW Grossman: Todos los caminos conducen a Paul Erdös. Rev. Acad. Colomb. Cieñe. 23(89):563-582, 1999. ...
Scientific Annals of Computer Science, 2014
Revista Colombiana de Matemáticas
In this paper some properties, examples and counterexamples about the formal derivative operator ... more In this paper some properties, examples and counterexamples about the formal derivative operator defined with respect to context-free grammars are presented. In addition, we show a connection between the context-free grammar G = { a → abr; b → br+1 } and multifactorial numbers. Some identities involving multifactorial numbers will be obtained by grammatical methods.
In this paper we introduce a family of infinite words that generalize the Fibonacci word and we s... more In this paper we introduce a family of infinite words that generalize the Fibonacci word and we study their combinatorial properties. We associate with this family of words a family of curves that are like the Fibonacci word fractal and reveal some fractal features. Finally, we describe an infinite family of polyominoes stems from the generalized Fibonacci words and we study some of their geometric properties, such as perimeter and area. These last polyominoes generalize the Fibonacci snowflake and they are double squares polyominoes, i.e., tile the plane by translation in exactly two distinct ways.
Theoretical Computer Science, 2014
In this paper we introduce a family of infinite words that generalize the Fibonacci word and we s... more In this paper we introduce a family of infinite words that generalize the Fibonacci word and we study their combinatorial properties. We associate with this family of words a family of curves that are like the Fibonacci word fractal and reveal some fractal features. Finally, we describe an infinite family of polyominoes stems from the generalized Fibonacci words and we study some of their geometric properties, such as perimeter and area. These last polyominoes generalize the Fibonacci snowflake and they are double squares polyominoes, i.e., tile the plane by translation in exactly two distinct ways.
In this paper we introduce a family of infinite words that generalize the Fibonacci word and we s... more In this paper we introduce a family of infinite words that generalize the Fibonacci word and we study their combinatorial properties. Moreover, we associate to this family of words a family of curves, which have fractal properties, in particular these curves have as attractor the Fibonacci word fractal. Finally, we describe an infinite family of polyominoes (double squares) from the generalized Fibonacci words and we study some of their geometric properties. These last polyominoes generalize the Fibonacci snowflake.
Boletin De Matematicas, 2004
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Books by Rodrigo De Castro Korgi
Papers by Rodrigo De Castro Korgi