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Book DetailsContemporary MathematicsVolume: 558; 2011; 519 ppMSC: Primary 03; 05; 68;
This volume contains the proceedings of the AMSASL Special Session on Model Theoretic Methods in Finite Combinatorics, held January 5–8, 2009, in Washington, DC.
Over the last 20 years, various new connections between model theory and finite combinatorics emerged. The best known of these are in the area of 01 laws, but in recent years other very promising interactions between model theory and combinatorics have been developed in areas such as extremal combinatorics and graph limits, graph polynomials, homomorphism functions and related counting functions, and discrete algorithms, touching the boundaries of computer science and statistical physics.
This volume highlights some of the main results, techniques, and research directions of the area. Topics covered in this volume include recent developments on 01 laws and their variations, counting functions defined by homomorphisms and graph polynomials and their relation to logic, recurrences and spectra, the logical complexity of graphs, algorithmic meta theorems based on logic, universal and homogeneous structures, and logical aspects of Ramsey theory.ReadershipGraduate students and research mathematicians interested in logic, combinatorics, and theoretical computer science.

Table of Contents

Articles

Eldar Fischer, Tomer Kotek and Johann A. Makowsky  Application of logic to combinatorial sequences and their recurrence relations

Jason P. Bell, Stanley N. Burris and Karen Yeats  Spectra and systems of equations

Jason P. Bell and Stanley N. Burris  Compton’s method for proving logical limit laws

Oleg Pikhurko and Oleg Verbitsky  Logical complexity of graphs: A survey

Martin Grohe and Stephan Kreutzer  Methods for algorithmic meta theorems

Tomer Kotek, Johann A. Makowsky and Boris Zilber  On counting generalized colorings

Martin Grohe and Marc Thurley  Counting homomorphisms and partition functions

Jan Hubička and Jarošlav Nešetřil  Some examples of universal and generic partial orders

Gregory Cherlin  Two problems on homogeneous structures, revisited

Assaf Hasson, Menachem Kojman and Alf Onshuus  On symmetric indivisbility of countable structures

Andreas Blass  Partitions and permutation groups

Dietrich Kuske  (Un)countable and (non)effective versions of Ramsey’s theorem

Manuel Bodirsky and Michael Pinsker  Reducts of Ramsey structures


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This volume contains the proceedings of the AMSASL Special Session on Model Theoretic Methods in Finite Combinatorics, held January 5–8, 2009, in Washington, DC.
Over the last 20 years, various new connections between model theory and finite combinatorics emerged. The best known of these are in the area of 01 laws, but in recent years other very promising interactions between model theory and combinatorics have been developed in areas such as extremal combinatorics and graph limits, graph polynomials, homomorphism functions and related counting functions, and discrete algorithms, touching the boundaries of computer science and statistical physics.
This volume highlights some of the main results, techniques, and research directions of the area. Topics covered in this volume include recent developments on 01 laws and their variations, counting functions defined by homomorphisms and graph polynomials and their relation to logic, recurrences and spectra, the logical complexity of graphs, algorithmic meta theorems based on logic, universal and homogeneous structures, and logical aspects of Ramsey theory.
Graduate students and research mathematicians interested in logic, combinatorics, and theoretical computer science.

Articles

Eldar Fischer, Tomer Kotek and Johann A. Makowsky  Application of logic to combinatorial sequences and their recurrence relations

Jason P. Bell, Stanley N. Burris and Karen Yeats  Spectra and systems of equations

Jason P. Bell and Stanley N. Burris  Compton’s method for proving logical limit laws

Oleg Pikhurko and Oleg Verbitsky  Logical complexity of graphs: A survey

Martin Grohe and Stephan Kreutzer  Methods for algorithmic meta theorems

Tomer Kotek, Johann A. Makowsky and Boris Zilber  On counting generalized colorings

Martin Grohe and Marc Thurley  Counting homomorphisms and partition functions

Jan Hubička and Jarošlav Nešetřil  Some examples of universal and generic partial orders

Gregory Cherlin  Two problems on homogeneous structures, revisited

Assaf Hasson, Menachem Kojman and Alf Onshuus  On symmetric indivisbility of countable structures

Andreas Blass  Partitions and permutation groups

Dietrich Kuske  (Un)countable and (non)effective versions of Ramsey’s theorem

Manuel Bodirsky and Michael Pinsker  Reducts of Ramsey structures