Combinatorics: topics, techniques, algorithms
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
1994
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 355 S. graph. Darst. |
| ISBN: | 0521457610 0521451337 |
Internformat
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| 245 | 1 | 0 | |a Combinatorics |b topics, techniques, algorithms |c Peter J. Cameron |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 1994 | |
| 300 | |a VIII, 355 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804124284500574208 |
|---|---|
| adam_text | Contents
Preface ix
1. What is Combinatorics? 1
Sample problems — How to use this book — What you need to know — Exercises
2. On numbers and counting 7
Natural numbers and arithmetic — Induction — Some useful functions — Orders
of magnitude — Different ways of counting — Double counting — Appendix on
set notation — Exercises
3. Subsets, partitions, permutations 21
Subsets — Subsets of fixed size — The Binomial Theorem and Pascal s Triangle
— Project: Congruences of binomial coefficients — Permutations — Estimates for
factorials — Selections — Equivalence and order — Project: Finite topologies —
Project: Cayley s Theorem on trees — Bell numbers — Generating combinatorial
objects — Exercises
4. Recurrence relations and generating functions 49
Fibonacci numbers — Aside on formal power series — Linear recurrence relations
with constant coefficients — Derangements and involutions — Catalan and Bell
numbers — Computing solutions to recurrence relations — Project: Finite fields
and QUICKSORT — Exercises
5. The Principle of Inclusion and Exclusion 75
PIE — A generalisation — Stirling numbers — Project: Stirling numbers and
exponentials — Even and odd permutations — Exercises
6. Latin squares and SDRs 87
Latin squares — Systems of distinct representatives — How many Latin squares?
— Quasigroups — Project: Quasigroups and groups — Orthogonal Latin squares
— Exercises
7. Extremal set theory 99
Intersecting families — Sperner families — The De Bruijn Erdos Theorem —
Project: Regular families — Exercises
8. Steiner triple systems 107
Steiner systems — A direct construction — A recursive construction — Packing and
covering — Project: Some special Steiner triple systems — Project: Tournaments
and Kirkman s schoolgirls — Exercises
9. Finite geometry 123
Linear algebra over finite fields — Gaussian coefficients — Projective geometry —
Axioms for projective geometry — Projective planes — Other kinds of geometry
— Project: Coordinates and configurations — Project: Proof of the Bruck Ryser
Theorem — Appendix: Finite fields — Exercises
10. Ramsey s Theorem 147
The Pigeonhole Principle — Some special cases — Ramsey s Theorem — Bounds
for Ramsey numbers — Applications — The infinite version — Exercises
viii Contents
11. Graphs 159
Definitions — Trees and forests — Minimal spanning trees — Eulerian graphs
— Hamiltonian graphs — Project: Gray codes — The Travelling Salesman —
Digraphs — Networks — Menger, Konig and Hall — Diameter and girth —
Project: Moore graphs — Exercises
12. Posets, lattices and matroids 187
Posets and lattices — Linear extensions of a poset — Distributive lattices —
Aside on propositional logic — Chains and antichains — Products and dimension
— The Mobius function of a poset — Matroids — Project: Arrow s Theorem —
Exercises
13. More on partitions and permutations 209
Partitions, diagrams and conjugacy classes — Euler s Pentagonal Numbers
Theorem — Project: Jacobi s Identity — Tableaux — Symmetric polynomials —
Exercises
14. Automorphism groups and permutation groups 225
Three definitions of a group — Examples of groups — Orbits and transitivity —
The Schreier Sims algorithm — Primitivity and multiple transitivity — Examples
— Project: Cayley digraphs and Frucht s Theorem — Exercises
15. Enumeration under group action 245
The Orbit counting Lemma — An application — Cycle index — Examples —
Direct and wreath products — Stirling numbers revisited — Project: Cycle index
and symmetric functions — Exercises
16. Designs 257
Definitions and examples — To repeat or not to repeat — Fisher s Inequality —
Designs from finite geometry — Small designs — Project: Hadamard matrices —
Exercises
17. Error correcting codes 271
Finding out a liar — Definitions — Probabilistic considerations — Some bounds
— Linear codes; Hamming codes — Perfect codes — Linear codes and projective
spaces — Exercises
18. Graph colourings 291
More on bipartite graphs — Vertex colourings — Project: Brooks Theorem —
Perfect graphs — Edge colourings — Topological graph theory — Project: The
Five colour Theorem — Exercises
19. The infinite 307
Counting infinite sets — Konig s Infinity Lemma — Posets and Zorn s Lemma —
Ramsey theory — Systems of distinct representatives — Free constructions — The
random graph — Exercises
20. Where to from here? 325
Computational complexity — Some graph theoretic topics — Computer software
— Unsolved problems — Further reading
Answers to selected exercises 339
Bibliography 343
Index 347
|
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| genre | Lehrbuch - Kombinatorik |
| genre_facet | Lehrbuch - Kombinatorik |
| id | DE-604.BV009920273 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:43:13Z |
| institution | BVB |
| isbn | 0521457610 0521451337 |
| language | English |
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| physical | VIII, 355 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Cambridge Univ. Press |
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| spelling | Cameron, Peter J. 1947- Verfasser (DE-588)120275929 aut Combinatorics topics, techniques, algorithms Peter J. Cameron 1. ed. Cambridge Cambridge Univ. Press 1994 VIII, 355 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kombinatorik (DE-588)4031824-2 gnd rswk-swf Lehrbuch - Kombinatorik Kombinatorik (DE-588)4031824-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006571062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cameron, Peter J. 1947- Combinatorics topics, techniques, algorithms Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4031824-2 |
| title | Combinatorics topics, techniques, algorithms |
| title_auth | Combinatorics topics, techniques, algorithms |
| title_exact_search | Combinatorics topics, techniques, algorithms |
| title_full | Combinatorics topics, techniques, algorithms Peter J. Cameron |
| title_fullStr | Combinatorics topics, techniques, algorithms Peter J. Cameron |
| title_full_unstemmed | Combinatorics topics, techniques, algorithms Peter J. Cameron |
| title_short | Combinatorics |
| title_sort | combinatorics topics techniques algorithms |
| title_sub | topics, techniques, algorithms |
| topic | Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Kombinatorik Lehrbuch - Kombinatorik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006571062&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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