Titre :	A walk through combinatorics : an introduction to enumeration and graph theory
Type de document :	texte imprimé
Auteurs :	Bona , Miklos, Auteur
Editeur :	Singapore : World Scientific
Année de publication :	2002
Importance :	XVII, 406 p.
Présentation :	ill.
Format :	24 cm
ISBN/ISSN/EAN :	978-981-02-4900-7
Note générale :	Bibliogr. p. 401-402. - Index
Langues :	Anglais (eng)
Mots-clés :	Graph theory Combinatorial analysis Graphes, Théorie des
Index. décimale :	519.17 Théorie des graphes
Résumé :	This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of exercises, ranging in difficulty from "routine" to "worthy of independent publication", is included. In each section, there are also exercises that contain material not explicitly discussed in the text before, so as to provide instructors with extra choices if they want to shift the emphasis of their course.It goes without saying that the text covers the classic areas, i.e. combinatorial choice problems and graph theory. What is unusual, for an undergraduate textbook, is that the author has included a number of more elaborate concepts, such as Ramsey theory, the probabilistic method and -- probably the first of its kind -- pattern avoidance. While the reader can only skim the surface of these areas, the author believes that they are interesting enough to catch the attention of some students. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.
Note de contenu :	Summary : I : Basic methods 1. Seven is more than six. The pigeon-hole principle 2. One step at a time. The method of mathematical induction II : Enumerative combinatorics 3. There are a lot of them. Elementary counting problems 4. No matter how you slice it. The binomial theorem and related identities 5. Divide and conquer. Partitions 6. Not so vicious cycles. Cycles in permutations 7. You shall not overcount. The sieve 8. A function is worth many numbers. Generating functions III : Graph theory 9. Dots and lines. The origins of graph theory 10. Staying connected. Trees 11. Finding a good match. Coloring and matching 12. Do not cross. Planar graphs Iv : horizons 13. Does it clique? Ramsey theory 14. So hard to avoid. Subsequence conditions on permutations 15. Who knows what it looks like, but it exists. The probabilistic method 16. At least some order. Partial orders

A walk through combinatorics : an introduction to enumeration and graph theory [texte imprimé] / Bona , Miklos, Auteur . - Singapore : World Scientific, 2002 . - XVII, 406 p. : ill. ; 24 cm.
ISBN : 978-981-02-4900-7
Bibliogr. p. 401-402. - Index
Langues : Anglais (eng)

Mots-clés :	Graph theory Combinatorial analysis Graphes, Théorie des
Index. décimale :	519.17 Théorie des graphes
Résumé :	This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of exercises, ranging in difficulty from "routine" to "worthy of independent publication", is included. In each section, there are also exercises that contain material not explicitly discussed in the text before, so as to provide instructors with extra choices if they want to shift the emphasis of their course.It goes without saying that the text covers the classic areas, i.e. combinatorial choice problems and graph theory. What is unusual, for an undergraduate textbook, is that the author has included a number of more elaborate concepts, such as Ramsey theory, the probabilistic method and -- probably the first of its kind -- pattern avoidance. While the reader can only skim the surface of these areas, the author believes that they are interesting enough to catch the attention of some students. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.
Note de contenu :	Summary : I : Basic methods 1. Seven is more than six. The pigeon-hole principle 2. One step at a time. The method of mathematical induction II : Enumerative combinatorics 3. There are a lot of them. Elementary counting problems 4. No matter how you slice it. The binomial theorem and related identities 5. Divide and conquer. Partitions 6. Not so vicious cycles. Cycles in permutations 7. You shall not overcount. The sieve 8. A function is worth many numbers. Generating functions III : Graph theory 9. Dots and lines. The origins of graph theory 10. Staying connected. Trees 11. Finding a good match. Coloring and matching 12. Do not cross. Planar graphs Iv : horizons 13. Does it clique? Ramsey theory 14. So hard to avoid. Subsequence conditions on permutations 15. Who knows what it looks like, but it exists. The probabilistic method 16. At least some order. Partial orders