Contemporary Mathematics
Application of Logic to Combinatorial Sequences
and
Their Recurrence Relations
Eldar Fischer, Tomer Kotek, and Johann A. Makowsky
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 ole of logic
15. Structures of bounded degree
16. Structures of unbounded degree
References
2010 Mathematics Subject Classification. 03-02, 03C98, 05-02, 05A15, 11B50 .
Partially supported by an ISF grant number 1101/06 and an ERC-2007-StG grant number
202405.
Partially supported by the Fein Foundation and the Graduate School of the Technion - Israel
Institute of Technology.
Partially supported by the Israel Science Foundation for the project “Model Theoretic Inter-
pretations of Counting Functions” (2007-2010) and the Grant for Promotion of Research by the
Technion–Israel Institute of Technology.
2011 American Mathematical Society
1
Contemporary Mathematics
Volume 558, 2011
cc 2011 American Mathematical Society
1
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