Verfügbarkeit: Combinatorial mathematics | Technische Universität München

Combinatorial mathematics:

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Bibliographische Detailangaben
Beteilige Person:	West, Douglas Brent (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Cambridge Cambridge University Press 2021
Schlagwörter:	Planarer Graph Teilweise Ordnung Abzählende Kombinatorik Ramsey-Theorie Matching > Graphentheorie Kombinatorik Graphfärbung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032204566&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Enthält Literaturverzeichnis Seite 849-928 und Indexe
Umfang:	xx, 969 Seiten Illustrationen, Diagramme
ISBN:	9781107058583

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Datensatz im Suchindex

DE-BY-TUM_call_number	0202 MAT 050 2020 B 1080
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adam_text	Contents xiii Preface Chapter 0 - Introduction. 1 Sets, Functions, and Relations: 2. Graphs: 3. Discrete Probability: 6, Other Discrete Structures: 8. Complexity: 9. Part I — Enumeration Chapter 1 - Combinatorial Arguments. 13 1.1. Classical Models. Elementary Principles: 14. Words, Sets, and Multisets: 16. Exercises: 20. 1.2. Identities. Lattice Paths and Pascal’s Triangle: 24. Delannoy Numbers: 28. Exercises: 31. 1.3. Applications. Graphs and Trees: 35. Multinomial Coefficients: 37. The Ballot Problem: 39. Catalan Numbers: 41. Exercises: 46. 14 Chapter 2 - Recurrence Relations. 51 2.1. Obtaining Recurrences. Classical Examples: 52. Variations: 56. Exercises: 59. 2.2. Elementary Solution Methods. The Characteristic Equation Method: 67. The Generating Function Method: 73. Exercises: 78. 2.3. Further Topics. The Substitution Method: 82. Asymptotic Analysis: 84. The WZ Method (optional): 87. Exercises: 91. 52 vii 24 35 66 82 viii Contents Chapter 3 - Generating Functions. 93 3.1. Ordinary Generating Functions. Modeling Counting Problems: 94. Permutation Statistics: 98. Exercises: 103. 3.2. Coefficients and Applications. Operations and Summations: 107. Snake Oil: 112. Exercises: 114. 3.3. Exponential Generating Functions. Modeling Labeled Structures: 118. Stirling and Derangement Applications: 121. The Exponential Formula: 124. The Lagrange Inversion Formula (optional): 129. Exercises: 132. 3.4. Partitions of Integers. Generating Function Methods: 137. Ferrers Diagrams: 141. Bulgarian Solitaire (optional): 143. Distribution Models: 145. Exercises: 148. 93 Chapter 4 - Further Topics. 4.1. The Inclusion-Exclusion Principle. The Basic Principle: 153. Restricted Permutations: 159. Signed Involutions: 163. Determinants and Path Systems (optional): 165. Exercises: 171. 4.2. Pólya-Redfield Counting. Burnside’s Lemma: 179. The Pattern Inventory: 181. Classical Cycle Indices: 185. Exercises: 187. 4.3. Permutations and Tableaux. The Hook-Length Formula: 189. The RSK Correspondence: 193. Switching Р-Symbol and Q-Symbol: 198. Jeu de Taquin (optional): 201. Exercises: 206. 107 118 137 153 153 178 189 Part II — Graphs Chapter 5 - First Concepts for Graphs. 5.1. Definitions and Examples. Graphs and Subgraphs: 209. Isomorphism: 211. The Petersen Graph and Hypercubes: 213. Exercises: 216. 5.2. Vertex Degrees. The Degree-Sum Formula: 220. Degree Lists: 221. Extremality: 223. Directed Graphs: 224. Exercises: 226. 5.3. Connection and Decomposition. Components and Walks: 229. Cycles and Cut-Edges: 231. Eulerian Circuits: 233. Exercises: 235. 5.4. Trees and Distance. Properties of Trees: 240. Distance and Diameter: 242. Optimization on Weighted Graphs: 245. Exercises: 247. 209 209 220 229 239 Contents Chapter 6 - Matchings. 6.1. Matching in Bipartite Graphs. Hall’s Theorem: 254. Min-Max Relations: 258. Exercises: 260. 6.2. Matching in General Graphs. Tutte’s 1-Factor Theorem: 264. General Factors of Graphs: 268. Exercises: 272. 6.3. Algorithmic Aspects. Augmenting Paths: 277. Weighted Bipartite Matching: 279. Fast Bipartite Matching (optional): 283. Stable Matchings (optional): 284. Exercises: 286. Chapter 7 - Connectivity and Cycles. ix 253 253 264 276 289 7.1. Connectivity Parameters. 289 Separating Sets: 289. Edge Cuts: 293. Blocks: 294. Exercises: 295. 7.2. Properties of ¿-Connected Graphs. 298 Menger’s Theorem: 298. Applications of Menger’s Theorem: 301. 2-Connected and З-Connected Graphs: 304. Highly Connected Orientations (optional): 307. Exercises: 311. 7.3. Spanning Cycles. 316 Properties of Hamiltonian Graphs: 317. Sufficient Conditions: 319. Long Cycles (optional): 322. Further Directions (optional): 325. Exercises: 328. Chapter 8 - Coloring. 8.1. Vertex Coloring. Upper Bounds: 336. Triangle-Free Graphs: 339. Exercises: 341. 8.2. Structural Aspects. Color-Critical Graphs: 344. List Coloring: 346. Forced Subgraphs (optional): 349. Exercises: 353. 8.3. Edge-Coloring and Perfection. Special Classes: 357. Vizing’s Theorem and Extensions: 359. List Edge-Coloring: 362. Perfect Graphs: 366. Exercises: 370. Chapter 9 - Planar Graphs. 335 335 344 357 377 9.1. Embeddings and Euler’s Formula. 377 Drawings and Duals: 378. Euler’s Formula: 383. Exercises: 385. 9.2. Structure of Planar Graphs. 390 Kuratowski’s Theorem: 390. The Separator Theorem (optional): 394. Exercises: 397. 9.3. Coloring of Planar Graphs. 399 Edge-Colorings and Spanning Cycles: 400. 5-Colorable and 5-Choosable: 402. The Four Color Problem: 404. Discharging and Light Edges: 407. Other Aspects of Discharging (optional): 412. Exercises: 417. x Contents Part III — Sets Chapter 10 - Ramsey Theory. 425 10.1. The Pigeonhole Principle. 425 Classical Applications: 426. Monotone Sublists: 430. Pattern-Avoiding Permutations (optional): 431. Large Girth and Chromatic Number (optional): 434. Edge-Coloring of Hypergraphs (optional): 438. Exercises: 440. 10.2. Ramsey’s Theorem. 443 The Main Theorem: 443. Applications: 445. Ramsey Numbers: 448. Graph Ramsey Theory: 453. Exercises: 458. 10.3. Further Topics. 461 Van der Waerden’s Theorem: 461. Infinite Sets (optional): 468. The Canonical Ramsey Theorem (optional): 470. Exercises: 473. Chapter 11 - Extremal Problems. 475 11.1. Forced Subgraphs. 475 Turán’s Theorem: 475. Erdős-Stone Theorem: 478. Linear Ramsey for Bounded Degree: 483. Roth’s Theorem: 484. Proof of the Regularity Lemma (optional): 486. Exercises: 489. 11.2. Families of Sets. 493 The Kruskal-Katona Theorem: 493. Antichains and Intersecting Families: 496. Chvátal’s Conjecture: 501. Sunflowers (optional): 503. Entropy (optional): 504. Exercises: 510. 11.3. Matroids. 513 Hereditary Systems and Examples: 514. Axiomatics of Matroids: 519. Duality and Minors: 523. The Span Function: 527. Matroid Intersection: 529. Matroid Union: 533. Exercises: 536. Chapter 12 - Partially Ordered Sets. 541 12.1. Structure of Posets. Definitions and Examples: 541. Dilworth’s Theorem and Beyond: 546. Exercises: 549. 12.2. Symmetric Chains and LYM Orders. Graded Posets: 552. Symmetric Chain Decompositions: 553. LYM and Sperner Properties: 558. Products of LYM Orders (optional): 562. Exercises: 564. 12.3. Linear Extensions and Dimension. Order Dimension: 569. Computation and Bounds: 572. Bipartite Posets: 575. Exercises: 582. 12.4. Special Families of Posets. Semiorders and Interval Orders: 585. Lattices: 588. Distributive Lattices: 591. Correlational Inequalities: 595. A Problem in Ramsey Theory (optional): 601. Exercises: 604. 541 552 568 585 Contents Chapter 13 - Combinatorial Designs. xi 609 13.1. Arrangements. 609 Latin Squares: 609. Block Designs: 612. Symmetric Designs: 615. Hadamard Matrices: 618. Exercises: 622. 13.2. Projective Planes. 624 Relation to Designs: 624. Applications to Extremal Problems: 628. Difference Sets: 634. Exercises: 638. 13.3. Further Constructions. 640 Steiner Triple Systems: 641. Graphical Designs: 645. Resolvable Designs and Other Tools: 648. The Euler Conjecture (optional): 651. Exercises: 654. Part IV — Methods Chapter 14 - The Probabilistic Method. 657 14.1. Existence and Expectation. The Union Bound: 658. Random Variables: 662. Exercises: 666. 14.2. Refinements of Basic Methods. Deletions and Alterations: 670. The Symmetric Local Lemma: 674. The General Local Lemma (optional): 679. Exercises: 684. 14.3. Moments and Thresholds. “Almost Always”: 687. Threshold Functions: 690. Convergenceof Moments: 694. Graph Evolution: 698. Exercises: 702. 14.4. Concentration Inequalities. Chebyshev and Chernoff Bounds: 706. Martingales: 712. Bounded Differences (optional): 719. Exercises: 721. 657 Chapter 15 - Linear Algebra. 670 686 706 723 15.1. Dimension and Polynomials. 723 The Dimension Argument: 723. Restricted Intersections of Sets (optional): 727. Combinatorial Nullstellensatz: 732. The Alon-Tarsi Theorem: 738. Exercises: 744. 15.2. Matrices. 747 Determinants and Trees: 747. Cycle Space and Bond Space: 752. Permanents and Planar Graphs: 754. Möbius Inversion (optional): 757. Exercises: 762. 15.3. Eigenvalues. 766 Spectra of Graphs: 766. Eigenvalues and Graph Parameters: 768. Regular and Strongly Regular Graphs: 772. Laplacian Eigenvalues: 776. Exercises: 780. xii Chapter 16 - Geometry and Topology. Contents 783 783 16.1. Graph Drawings. Embeddings on Grids: 783. Crossing Number: 790. Exercises: 797. 798 16.2. Combinatorial Topology. Sperner’s Lemma and Bandwidth: 799. Equivalent Topological Lemmas: 802. The Borsuk-Ulam Theorem: 806. Kneser Conjecture and Gale’s Lemma: 811. Ham Sandwiches and Bisections: 815. Borsuk’s Conjecture: 817. Exercises: 818. 821 16.3. Volumes and Containment. Monotone Subsequences: 821. Balanced Comparisons: 822. Containment Orders: 828. Exercises: 831. Hints to Selected Exercises 833 References 849 Author Index 929 Glossary of Notation 943 Subject Index 949
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spellingShingle	West, Douglas Brent Combinatorial mathematics Planarer Graph (DE-588)4174783-5 gnd Teilweise Ordnung (DE-588)4373793-6 gnd Abzählende Kombinatorik (DE-588)4132720-2 gnd Ramsey-Theorie (DE-588)4212682-4 gnd Matching Graphentheorie (DE-588)4831446-8 gnd Kombinatorik (DE-588)4031824-2 gnd Graphfärbung (DE-588)4472286-2 gnd
subject_GND	(DE-588)4174783-5 (DE-588)4373793-6 (DE-588)4132720-2 (DE-588)4212682-4 (DE-588)4831446-8 (DE-588)4031824-2 (DE-588)4472286-2
title	Combinatorial mathematics
title_auth	Combinatorial mathematics
title_exact_search	Combinatorial mathematics
title_full	Combinatorial mathematics Douglas B. West (Zhejiang Normal University, China and University of Illinois, Urbana-Champaign)
title_fullStr	Combinatorial mathematics Douglas B. West (Zhejiang Normal University, China and University of Illinois, Urbana-Champaign)
title_full_unstemmed	Combinatorial mathematics Douglas B. West (Zhejiang Normal University, China and University of Illinois, Urbana-Champaign)
title_short	Combinatorial mathematics
title_sort	combinatorial mathematics
topic	Planarer Graph (DE-588)4174783-5 gnd Teilweise Ordnung (DE-588)4373793-6 gnd Abzählende Kombinatorik (DE-588)4132720-2 gnd Ramsey-Theorie (DE-588)4212682-4 gnd Matching Graphentheorie (DE-588)4831446-8 gnd Kombinatorik (DE-588)4031824-2 gnd Graphfärbung (DE-588)4472286-2 gnd
topic_facet	Planarer Graph Teilweise Ordnung Abzählende Kombinatorik Ramsey-Theorie Matching Graphentheorie Kombinatorik Graphfärbung
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