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Model Theoretic Methods in Finite Combinatorics

Author: Martin Grohe; Johann A Makowsky; AMS-ASL Joint Special Session on Model Theoretic Methods in Finite Combinatorics; Association for Symbolic Logic,; American Mathematical Society,
Publisher: Providence : American Mathematical Society, 2011.
Series: Contemporary Mathematics.
Edition/Format:   eBook : Document : English
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Genre/Form: Electronic books
Conference papers and proceedings
Congresses
Additional Physical Format: Print version:
Grohe, Martin.
Model Theoretic Methods in Finite Combinatorics.
Providence : American Mathematical Society, ©2011
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Martin Grohe; Johann A Makowsky; AMS-ASL Joint Special Session on Model Theoretic Methods in Finite Combinatorics; Association for Symbolic Logic,; American Mathematical Society,
ISBN: 0821849433 9780821849439 9780821882375 0821882376 9780821883228 0821883224
OCLC Number: 990583781
Language Note: English.
Notes: Description based upon print version of record.
Description: 1 online resource (529 p.)
Contents: ""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""
Series Title: Contemporary Mathematics.
Other Titles: Contemporary Mathematics
Contemporary Mathematics, Volume 558
Model theoretic methods in finite combinatorics: AMS-ASL special session, January 5-8, 2009 Washington, DC

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