Overview of some general results in combinatorial enumeration

2008/03/29 by Martin Klazar, Klazar, Martin · 1 citation
Computer Science · Mathematics · #05A15 #05A16 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO #msc:05A15 #msc:05A16 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0803.4292

Submitted, minus Section 3.4, to the proceedings of the conference Permutation Patterns 2007. 42 pages

arxiv created 2008/03/29 · openalex publication_date 2008/03/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and hypergraphs, relational structures, and others. The second part advertises five topics in general enumeration: 1. counting lattice points in lattice polytopes, 2. growth of context-free languages, 3. holonomicity (i.e., P-recursiveness) of numbers of labeled regular graphs, 4. frequent occurrence of the asymptotics cn^-3/2rⁿ and 5. ultimate modular periodicity of numbers of MSOL-definable structures.

Citations

• The Profile of relations
• Spectra of monadic second order sentences
• Some relational structures with polynomial growth and their associated algebras
• Simple permutations and pattern restricted permutations
• On the growth rate of minor-closed classes of graphs
• Groups of Intermediate Growth: an Introduction for Beginners
• On growth rates of permutations, set partitions, ordered graphs and other objects

Cited by

• Effective formulas for linear recurrence sequences of integers

Related

• Enumerative Combinatorics
• Complexity problems in enumerative combinatorics
• Combinatorics
• Algebraic and geometric methods in enumerative combinatorics
• The many faces of modern combinatorics