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Produktbild: Mathematics of Ramsey Theory
Band 5

Mathematics of Ramsey Theory

Aus der Reihe Algorithms and Combinatorics

99,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

25.02.2012

Herausgeber

Jaroslav Nesetril + weitere

Verlag

Springer Berlin

Seitenzahl

269

Maße (L/B/H)

24,2/17/1,6 cm

Gewicht

518 g

Auflage

Softcover reprint of the original 1st ed. 1990

Sprache

Englisch

ISBN

978-3-642-72907-2

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

25.02.2012

Herausgeber

Verlag

Springer Berlin

Seitenzahl

269

Maße (L/B/H)

24,2/17/1,6 cm

Gewicht

518 g

Auflage

Softcover reprint of the original 1st ed. 1990

Sprache

Englisch

ISBN

978-3-642-72907-2

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Mathematics of Ramsey Theory
  • Ramsey Theory Old and New.- 1. Ramsey Numbers.- 2. Transfinite Ramsey Theory.- 3. Chromatic Number.- 4. Classical Theorems.- 5. Other Classical Theorems.- 6. Structural Generalizations.- 7. Infinite Ramsey Theorem.- 8. Unprovability Results.- 9. Non-Standard Applications.- I. Classics.- Problems and Results on Graphs and Hypergraphs: Similarities and Differences.- 1. Extremal Problems of Turán Type.- 2. Density Problems.- 3. Ramsey’s Theorem.- 4. Ramsey-Turán Type Problems.- 5. Chromatic Numbers.- Note on Canonical Partitions.- II. Numbers.- On Size Ramsey Number of Paths, Trees and Circuits. II.- 1. Introduction.- 2. Proof of Theorem 1 — Part One.- 3. Proof of Theorem 1 — Part Two.- 4. Proof of Theorem 2.- 5. Proof of Theorem 3.- On the Computational Complexity of Ramsey-Type Problems.- 1. Introduction.- 2. NP-Complete Ramsey Problems.- 3. Polynomial-Bounded Ramsey Problems.- 4. Discussion.- Constructive Ramsey Bounds and Intersection Theorems for Sets.- 1. Introduction.- 2. Families of Sets with Prescribed Intersections.- 3. The Proof of Theorem 2.3.- 4. The Proof of Theorem 1.1.- Ordinal Types in Ramsey Theory and Well-Partial-Ordering Theory.- 1. Introduction.- 2. Sheaves.- 3. Ramsey Systems.- 4. Well-Partial-Ordering.- 5. Erdös-Szekeres Theorem.- 6. Ramsey Systems.- 7. Canonical Ramsey Theorem.- III. Structural Theory.- Partite Construction and Ramsey Space Systems.- 1. Introduction.- 2. Statement of Results.- 3. Partite Lemma.- 4. Partite Construction.- 5. Applications.- Graham-Rothschild Parameter Sets.- 1. Introduction.- 2. Parameter Sets and Parameter Words (Definition and Basic Examples).- 3. Hales-Jewett’s Theorem.- 4. Graham-Rothschild’s Theorem.- 5. Infinite Versions.- 6. Other Structures.- Shelah’s Proof of the Hales-Jewett Theorem.- IV. Noncombinatorial Methods.- Partitioning Topological Spaces.- 1. Introduction.- 2. Partitioning Singletons.- 3. Partitioning Pairs.- 4. Open Problems.- Topological Ramsey Theory.- 1. Introduction.- 2. Ramsey Spaces and Ellentuck’s Theorem.- 3. Finitary Consequences of Ellentuck Type Theorems.- 4. The Axiom of Choice and the Construction of Non-Ramsey Sets.- 5. Finite Dimensional Analogues of Ellentuck Type Theorems.- 6. Canonical Partitions.- Ergodic Theory and Configurations in Sets of Positive Density.- 1. Introduction.- 2. Correspondence Between Subsets of ?2 and ?2-Actions.- 3. Ergodic Averages for Subsets of ?2.- 4. First Application to Subsets of Positive Density in ?2.- 5. Proof of Theorem A.- 6. A Recurrence Property of ?2-Actions.- 7. Proof of Theorem B.- V. Variations and Applications.- Topics in Euclidean Ramsey Theory.- 1. Introduction.- 2. Preliminaries.- 3. Ramsey Sets.- 4. Sphere-Ramsey Sets.- 5. Concluding Remarks.- On Pisier Type Problems and Results (Combinatorial Applications to Number Theory).- 1. Introduction.- 2. Multiplicative Bases and Szemerédi-Ruzsa Theorem.- 3. Graphical Sequences and Examples of Their Use.- 4. Pisier Type Theorems.- 5. Pisier Problem — Positive Results.- 6. Special Ramsey Graphs — the Partite Construction.- Combinatorial Statements Independent of Arithmetic.- 1. Introduction.- 2. Notation.- 3. Arithmetic.- 4. Conclusions.- Boolean Complexity and Ramsey Theorems.- 1. General Remarks.- 2. An Example of a Lower Bound to Formula Size Complexity.- Uncrowded Graphs.- 1. Graphs.- 2. Hypergraphs.- 3. Heilbronn’s Conjecture.- Author Index.