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Título : Combinatorics and Graph Theory Tipo de documento: documento electrónico Autores: John Harris ; SpringerLink (Online service) ; Jeffry L. Hirst ; Michael Mossinghoff Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: XV, 381 p Il.: online resource ISBN/ISSN/DL: 978-0-387-79711-3 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical logic Discrete mathematics Combinatorics Logic and Foundations Clasificación: 51 Matemáticas Resumen: This book covers a wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline. The second edition includes many new topics and features: • New sections in graph theory on distance, Eulerian trails, and Hamiltonian paths. • New material on partitions, multinomial coefficients, and the pigeonhole principle. • Expanded coverage of Pólya Theory to include de Bruijn’s method for counting arrangements when a second symmetry group acts on the set of allowed colors. • Topics in combinatorial geometry, including Erdos and Szekeres’ development of Ramsey Theory in a problem about convex polygons determined by sets of points. • Expanded coverage of stable marriage problems, and new sections on marriage problems for infinite sets, both countable and uncountable. • Numerous new exercises throughout the book. About the First Edition: ". . . this is what a textbook should be! The book is comprehensive without being overwhelming, the proofs are elegant, clear and short, and the examples are well picked." — Ioana Mihaila, MAA Reviews Nota de contenido: Graph Theory -- Combinatorics -- Infinite Combinatorics and Graphs En línea: http://dx.doi.org/10.1007/978-0-387-79711-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34257 Combinatorics and Graph Theory [documento electrónico] / John Harris ; SpringerLink (Online service) ; Jeffry L. Hirst ; Michael Mossinghoff . - New York, NY : Springer New York, 2008 . - XV, 381 p : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-0-387-79711-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical logic Discrete mathematics Combinatorics Logic and Foundations Clasificación: 51 Matemáticas Resumen: This book covers a wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline. The second edition includes many new topics and features: • New sections in graph theory on distance, Eulerian trails, and Hamiltonian paths. • New material on partitions, multinomial coefficients, and the pigeonhole principle. • Expanded coverage of Pólya Theory to include de Bruijn’s method for counting arrangements when a second symmetry group acts on the set of allowed colors. • Topics in combinatorial geometry, including Erdos and Szekeres’ development of Ramsey Theory in a problem about convex polygons determined by sets of points. • Expanded coverage of stable marriage problems, and new sections on marriage problems for infinite sets, both countable and uncountable. • Numerous new exercises throughout the book. About the First Edition: ". . . this is what a textbook should be! The book is comprehensive without being overwhelming, the proofs are elegant, clear and short, and the examples are well picked." — Ioana Mihaila, MAA Reviews Nota de contenido: Graph Theory -- Combinatorics -- Infinite Combinatorics and Graphs En línea: http://dx.doi.org/10.1007/978-0-387-79711-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34257 Ejemplares
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Título : Combinatorics of Coxeter Groups Tipo de documento: documento electrónico Autores: Anders Bjorner ; SpringerLink (Online service) ; Francesco Brenti Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 231 Número de páginas: XIV, 366 p Il.: online resource ISBN/ISSN/DL: 978-3-540-27596-1 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Topological groups Lie Combinatorics Groups, Groups Theory and Generalizations Clasificación: 51 Matemáticas Resumen: Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxeter groups, such as reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory. While Coxeter groups have already been exposited from algebraic and geometric perspectives, this text is the first one to focus mainly on the combinatorial aspects of Coxeter groups. The first part of the book provides a self-contained introduction to combinatorial Coxeter group theory. The emphasis here is on the combinatorics of reduced decompositions, Bruhat order, weak order, and some aspects of root systems. The second part deals with more advanced topics, such as Kazhdan-Lusztig polynomials and representations, enumeration, and combinatorial descriptions of the classical finite and affine Weyl groups. A wide variety of exercises, ranging from easy to quite difficult are also included. The book will serve graduate students as well as researchers. Anders Björner is Professor of Mathematics at the Royal Institute of Technology in Stockholm, Sweden. Francesco Brenti is Professor of Mathematics at the University of Rome Nota de contenido: I -- The basics -- Bruhat order -- Weak order and reduced words -- Roots, games, and automata -- II -- Kazhdan-Lusztig and R-polynomials -- Kazhdan-Lusztig representations -- Enumeration -- Combinatorial Descriptions En línea: http://dx.doi.org/10.1007/3-540-27596-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35283 Combinatorics of Coxeter Groups [documento electrónico] / Anders Bjorner ; SpringerLink (Online service) ; Francesco Brenti . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - XIV, 366 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 231) .
ISBN : 978-3-540-27596-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Topological groups Lie Combinatorics Groups, Groups Theory and Generalizations Clasificación: 51 Matemáticas Resumen: Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxeter groups, such as reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory. While Coxeter groups have already been exposited from algebraic and geometric perspectives, this text is the first one to focus mainly on the combinatorial aspects of Coxeter groups. The first part of the book provides a self-contained introduction to combinatorial Coxeter group theory. The emphasis here is on the combinatorics of reduced decompositions, Bruhat order, weak order, and some aspects of root systems. The second part deals with more advanced topics, such as Kazhdan-Lusztig polynomials and representations, enumeration, and combinatorial descriptions of the classical finite and affine Weyl groups. A wide variety of exercises, ranging from easy to quite difficult are also included. The book will serve graduate students as well as researchers. Anders Björner is Professor of Mathematics at the Royal Institute of Technology in Stockholm, Sweden. Francesco Brenti is Professor of Mathematics at the University of Rome Nota de contenido: I -- The basics -- Bruhat order -- Weak order and reduced words -- Roots, games, and automata -- II -- Kazhdan-Lusztig and R-polynomials -- Kazhdan-Lusztig representations -- Enumeration -- Combinatorial Descriptions En línea: http://dx.doi.org/10.1007/3-540-27596-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35283 Ejemplares
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Título : Advances in Combinatorics : Waterloo Workshop in Computer Algebra, W80, May 26-29, 2011 Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Ilias S. Kotsireas ; Eugene V. Zima Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2013 Otro editor: Imprint: Springer Número de páginas: XX, 293 p Il.: online resource ISBN/ISSN/DL: 978-3-642-30979-3 Idioma : Inglés (eng) Palabras clave: Mathematics Computer mathematics Number theory Combinatorics Theory Computational and Numerical Analysis Clasificación: 51 Matemáticas Resumen: This volume, as Andrew M. Odlzyko writes in the foreword, “commemorates and celebrates the life and achievements of an extraordinary person.” Originally conceived as an 80th birthday tribute to Herbert Wilf, the well-known combinatorialist, the book has evolved beyond the proceeds of the W80 tribute. Professor Wilf was an award-winning teacher, who was supportive of women mathematicians, and who had an unusually high proportion of women among his PhD candidates. He was Editor-in-chief of the American Mathematical Monthly and a founder of both the Journal of Algorithms and of the Electronic Journal of Combinatorics. But he was first a researcher, driven by his desire to know and explain the inner workings of the mathematical world. The book collects high-quality, refereed research contributions by some of Professor Wilf’s colleagues, students, and collaborators. Many of the papers presented here were featured in the Third Waterloo Workshop on Computer Algebra (WWCA 2011, W80), held May 26-29, 2011 at Wilfrid Laurier University, Waterloo, Canada. Others were included because of their relationship to his important work in combinatorics. All are presented as a tribute to Herb Wilf’s contributions to mathematics and mathematical life Nota de contenido: Foreword by Andrew M. Odlyzko -- Glaisher’s formulas for 1/p2 and some generalizations: Gert Almkvist -- Complementary Bell numbers: Arithmetical properties and Wilf’s conjecture: Tewodros Amdeberhan and Valerio De Angelis and Victor H. Moll.- Partitions With Early Conditions: George E. Andrews -- Hypergeometric identities associated with statistics on words: George E. Andrews, Carla D. Savage, and Herbert S. Wilf -- Stationary Distribution and Eigenvalues for a de Bruijn Process: Arvind Ayyer and Volker Strehl -- Automatic Generation of Theorems and Proofs on Enumerating Consecutive-Wilf Classes: Andrew Baxter, Brian Nakamura, and Doron Zeilberger -- Watson–Like Formulae for Terminating 3F2-Series: Wenchang Chu and Roberta R. Zhou -- Balls in Boxes: Variations on a Theme of Warren Ewens and Herbert Wilf: Shalosh B. Ekhad and Doron Zeilberger -- Beating Your Fractional Beatty Game Opponent and: What’s the Question to Your Answer? Aviezri S. Fraenkel -- WZ-proofs of “divergent” Ramanujan-type series: Jesús Guillera -- Smallest parts in compositions: Arnold Knopfmacher and Augustine O. Munagi -- Cyclic Sieving for Generalised Non-Crossing Partitions Associated with Complex Reflection Groups of Exceptional Type: Christian Krattenthaler and ThomasW. M¨ uller -- Set partitions with no m-nesting: Marni Mishna and Lily Yen -- The distribution of zeros of the derivative of a random polynomial: Robin Pemantle and Igor Rivin -- On the distribution of small denominators in the Farey series of order N: C.L. Stewart -- Lost in translation: Wadim Zudilin En línea: http://dx.doi.org/10.1007/978-3-642-30979-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32507 Advances in Combinatorics : Waterloo Workshop in Computer Algebra, W80, May 26-29, 2011 [documento electrónico] / SpringerLink (Online service) ; Ilias S. Kotsireas ; Eugene V. Zima . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013 . - XX, 293 p : online resource.
ISBN : 978-3-642-30979-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer mathematics Number theory Combinatorics Theory Computational and Numerical Analysis Clasificación: 51 Matemáticas Resumen: This volume, as Andrew M. Odlzyko writes in the foreword, “commemorates and celebrates the life and achievements of an extraordinary person.” Originally conceived as an 80th birthday tribute to Herbert Wilf, the well-known combinatorialist, the book has evolved beyond the proceeds of the W80 tribute. Professor Wilf was an award-winning teacher, who was supportive of women mathematicians, and who had an unusually high proportion of women among his PhD candidates. He was Editor-in-chief of the American Mathematical Monthly and a founder of both the Journal of Algorithms and of the Electronic Journal of Combinatorics. But he was first a researcher, driven by his desire to know and explain the inner workings of the mathematical world. The book collects high-quality, refereed research contributions by some of Professor Wilf’s colleagues, students, and collaborators. Many of the papers presented here were featured in the Third Waterloo Workshop on Computer Algebra (WWCA 2011, W80), held May 26-29, 2011 at Wilfrid Laurier University, Waterloo, Canada. Others were included because of their relationship to his important work in combinatorics. All are presented as a tribute to Herb Wilf’s contributions to mathematics and mathematical life Nota de contenido: Foreword by Andrew M. Odlyzko -- Glaisher’s formulas for 1/p2 and some generalizations: Gert Almkvist -- Complementary Bell numbers: Arithmetical properties and Wilf’s conjecture: Tewodros Amdeberhan and Valerio De Angelis and Victor H. Moll.- Partitions With Early Conditions: George E. Andrews -- Hypergeometric identities associated with statistics on words: George E. Andrews, Carla D. Savage, and Herbert S. Wilf -- Stationary Distribution and Eigenvalues for a de Bruijn Process: Arvind Ayyer and Volker Strehl -- Automatic Generation of Theorems and Proofs on Enumerating Consecutive-Wilf Classes: Andrew Baxter, Brian Nakamura, and Doron Zeilberger -- Watson–Like Formulae for Terminating 3F2-Series: Wenchang Chu and Roberta R. Zhou -- Balls in Boxes: Variations on a Theme of Warren Ewens and Herbert Wilf: Shalosh B. Ekhad and Doron Zeilberger -- Beating Your Fractional Beatty Game Opponent and: What’s the Question to Your Answer? Aviezri S. Fraenkel -- WZ-proofs of “divergent” Ramanujan-type series: Jesús Guillera -- Smallest parts in compositions: Arnold Knopfmacher and Augustine O. Munagi -- Cyclic Sieving for Generalised Non-Crossing Partitions Associated with Complex Reflection Groups of Exceptional Type: Christian Krattenthaler and ThomasW. M¨ uller -- Set partitions with no m-nesting: Marni Mishna and Lily Yen -- The distribution of zeros of the derivative of a random polynomial: Robin Pemantle and Igor Rivin -- On the distribution of small denominators in the Farey series of order N: C.L. Stewart -- Lost in translation: Wadim Zudilin En línea: http://dx.doi.org/10.1007/978-3-642-30979-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32507 Ejemplares
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Título : Algebraic Combinatorics : Lectures at a Summer School in Nordfjordeid, Norway, June 2003 Tipo de documento: documento electrónico Autores: Peter Orlik ; SpringerLink (Online service) ; Volkmar Welker ; Gunnar Fløystad Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2007 Colección: Universitext, ISSN 0172-5939 Número de páginas: VIII, 182 p. 23 illus Il.: online resource ISBN/ISSN/DL: 978-3-540-68376-6 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Geometry Combinatorics Clasificación: 51 Matemáticas Nota de contenido: Lectures on Arrangements: Combinatorics and Topology -- Algebraic Combinatorics -- Applications -- Discrete Morse Theory and Free Resolutions -- Basic De.nitions and Examples -- Cellular Resolution -- Discrete Morse Theory En línea: http://dx.doi.org/10.1007/978-3-540-68376-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34650 Algebraic Combinatorics : Lectures at a Summer School in Nordfjordeid, Norway, June 2003 [documento electrónico] / Peter Orlik ; SpringerLink (Online service) ; Volkmar Welker ; Gunnar Fløystad . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007 . - VIII, 182 p. 23 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-3-540-68376-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Geometry Combinatorics Clasificación: 51 Matemáticas Nota de contenido: Lectures on Arrangements: Combinatorics and Topology -- Algebraic Combinatorics -- Applications -- Discrete Morse Theory and Free Resolutions -- Basic De.nitions and Examples -- Cellular Resolution -- Discrete Morse Theory En línea: http://dx.doi.org/10.1007/978-3-540-68376-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34650 Ejemplares
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Título : Algebraic Combinatorics : Walks, Trees, Tableaux, and More Tipo de documento: documento electrónico Autores: Richard P. Stanley ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: XII, 223 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-6998-8 Idioma : Inglés (eng) Palabras clave: Mathematics Combinatorics Graph theory Theory Clasificación: 51 Matemáticas Resumen: Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, de Bruijn sequences, the Erdos-Moser conjecture, electrical networks, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Pólya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhäuser Nota de contenido: Preface -- Notation.- 1. Walks in graphs -- 2. Cubes and the Radon transform -- 3. Random walks -- 4. The Sperner property -- 5. Group actions on boolean algebras -- 6. Young diagrams and q-binomial coefficients -- 7. Enumeration under group action -- 8. A glimpse of Young tableaux -- Appendix. The RSK algorithm -- Appendix. Plane partitions -- 9. The Matrix–Tree Theorem -- Appendix. Three elegant combinatorial proofs -- 10. Eulerian diagraphs and oriented trees -- 11. Cycles, bonds, and electrical networks -- 12. Miscellaneous gems of algebraic combinatorics -- Hints -- References En línea: http://dx.doi.org/10.1007/978-1-4614-6998-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32332 Algebraic Combinatorics : Walks, Trees, Tableaux, and More [documento electrónico] / Richard P. Stanley ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XII, 223 p : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-1-4614-6998-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Combinatorics Graph theory Theory Clasificación: 51 Matemáticas Resumen: Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, de Bruijn sequences, the Erdos-Moser conjecture, electrical networks, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Pólya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhäuser Nota de contenido: Preface -- Notation.- 1. Walks in graphs -- 2. Cubes and the Radon transform -- 3. Random walks -- 4. The Sperner property -- 5. Group actions on boolean algebras -- 6. Young diagrams and q-binomial coefficients -- 7. Enumeration under group action -- 8. A glimpse of Young tableaux -- Appendix. The RSK algorithm -- Appendix. Plane partitions -- 9. The Matrix–Tree Theorem -- Appendix. Three elegant combinatorial proofs -- 10. Eulerian diagraphs and oriented trees -- 11. Cycles, bonds, and electrical networks -- 12. Miscellaneous gems of algebraic combinatorics -- Hints -- References En línea: http://dx.doi.org/10.1007/978-1-4614-6998-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32332 Ejemplares
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