On the size of hereditary classes of graphs
Journal of Combinatorial Theory Series B
The speed of hereditary properties of graphs
Journal of Combinatorial Theory Series B
Advances in Applied Mathematics
The penultimate rate of growth for graph properties
European Journal of Combinatorics
Measures on monotone properties of graphs
Discrete Applied Mathematics
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
Recurrence relations for the number of labeled structures on a finite set
Proceedings of the Symposium "Rekursive Kombinatorik" on Logic and Machines: Decision Problems and Complexity
The Specker--Blatter theorem does not hold for quaternary relations
Journal of Combinatorial Theory Series A
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
The Art of Computer Programming, Volume 4, Fascicle 4: Generating All Trees--History of Combinatorial Generation (Art of Computer Programming)
Analytic Combinatorics
Practical Extrapolation Methods: Theory and Applications
Practical Extrapolation Methods: Theory and Applications
The specker-blatter theorem revisited
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Excluding Induced Subgraphs III: A General Asymptotic
Random Structures & Algorithms
A Representation Theorem for Holonomic Sequences Based on Counting Lattice Paths
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
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We consider functions of natural numbers which allow a combinatorial interpretation as counting functions (speed) of classes of relational structures, such as Fibonacci numbers, Bell numbers, Catalan numbers and the like. Many of these functions satisfy a linear recurrence relation over Z or Zm and allow an interpretation as counting the number of relations satisfying a property expressible in Monadic Second Order Logic (MSOL). C. Blatter and E. Specker (1981) showed that if such a function f counts the number of binary relations satisfying a property expressible in MSOL then f satisfies for every m ∈ N a linear recurrence relation over Zm. In this paper we give a complete characterization in terms of definability in MSOL of the combinatorial functions which satisfy a linear recurrence relation over Z, and discuss various extensions and limitations of the Specker-Blatter theorem.