Overview of some general results in combinatorial enumeration

Details Overview of some general results in combinatorial enumeration Overview of some general results in combinatorial enumeration

2008-03-29

arxiv.org/abs/0803.4292v1

Mathematics

Combinatorics

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

Scientific paper

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^{-3/2}r^n and 5. ultimate modular periodicity of numbers of MSOL-definable structures.

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