Model Theoretic Methods in Finite Combinatorics

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Grohe, Martin
Autores Corporativos: Association for Symbolic Logic (Content Provider.), American Mathematical Society (Content Provider.), AMS-ASL Joint Special Session on Model Theoretic Methods in Finite Combinatorics
Otros Autores: Makowsky, Johann A.
Formato: Electrónico Congresos, conferencias eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 2011.
Colección:Contemporary Mathematics.
Temas:
Finite model theory > Congresses.
Combinatorial probabilities > Congresses.
Combinatorial probabilities > Congresses.
Finite model theory > Congresses.
Théorie des modèles finis > Congrès.
Probabilités combinatoires > Congrès.
Combinatorial probabilities
Finite model theory
Mathematical logic and foundations > Research exposition (monographs, survey articles)
Mathematical logic and foundations > Proceedings, conferences, collections, etc.
Combinatorics > Research exposition (monographs, survey articles)
Combinatorics > Proceedings, conferences, collections, etc.
Computer science > Research exposition (monographs, survey articles)
Computer science > Proceedings, conferences, collections, etc.
Conference papers and proceedings
Acceso en línea:Texto completo
Tabla de Contenidos:
  • ""Contents""; ""Preface""; ""Application of Logic to Combinatorial Sequences and Their Recurrence Relations""; ""Part 1. Introduction and Synopsis""; ""1. Sequences of integers and their combinatorial interpretations""; ""2. Linear recurrences""; ""3. Logical formalisms""; ""4. Finiteness conditions""; ""5. Logical interpretations of integer sequences""; ""Part 2. Guiding Examples""; ""6. The classical recurrence relations""; ""7. Functions, permutations and partitions""; ""8. Trees and forests""; ""9. Graph properties""; ""10. Latin squares""; ""Part 3. C-Finite and Holonomic Sequences""
  • ""11. C-Finite sequences""""12. Holonomic sequences""; ""Part 4. Modular Recurrence Relations""; ""13. DU-index and Specker index""; ""14. The rÃ?le of logic""; ""15. Structures of bounded degree""; ""16. Structures of unbounded degree""; ""References""; ""Spectra and Systems of Equations""; ""Compton's Method for Proving Logical Limit Laws""; ""Logical Complexity of Graphs: A Survey""; ""1. Introduction""; ""1.1. Basic notions and examples""; ""1.2. Variations of logic""; ""1.3. Outline of the survey""; ""1.4. Other structures""; ""2. Preliminaries""; ""2.1. Notation: Arithmetic and graphs""
  • ""2.2. A length-depth relation""""2.3. Distinguishability vs. definability""; ""3. Ehrenfeucht games""; ""4. The Weisfeiler-Lehman algorithm""; ""5. Worst case bounds""; ""5.1. Classes of graphs""; ""5.2. General case""; ""6. Average case bounds""; ""Methods for Algorithmic Meta Theorems""; ""On Counting Generalized Colorings""; ""1. Introduction""; ""2. Prelude: two typical graph polynomials""; ""3. Counting generalized colorings""; ""4. SOL-polynomials and subset expansion""; ""5. Standard vs FF vs Newton SOL-polynomials""; ""6. Equivalence of counting Ï?-colorings and SOL-polynomials""
  • ""7. MSOL-polynomials""""8. Enter categoricity""; ""9. Conclusions""; ""References""; ""Counting Homomorphisms and Partition Functions""; ""Some Examples of Universal and Generic Partial Orders""; ""Two Problems on Homogeneous Structures, Revisited""; ""On Symmetric Indivisibility of Countable Structures""; ""Partitions and Permutation Groups""; ""(Un)countable and (Non)effective Versions of Ramsey's Theorem""; ""Reducts of Ramsey Structures""; ""1. Introduction""; ""2. Reducts""; ""3. Ramsey Classes""; ""4. Topological Dynamics""; ""5. Minimal Functions""; ""6. Decidability of Definability""
  • ""7. Interpretability""""8. Complexity of Constraint Satisfaction""; ""9. Concluding Remarks and Further Directions""; ""References""

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