Automatic enumeration of regular objects

Details Automatic enumeration of regular objects Automatic enumeration of regular objects

2005-07-12

arxiv.org/abs/math/0507249v2

Journal of Integer Sequences, Vol. 10 (2007), Article 07.5.5

Mathematics

Combinatorics

Corrected for readability; To appear in the Journal of Integer Sequences

Scientific paper

We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These differential equations are then used to determine the initial counting sequence and for asymptotic analysis. The key tool is the scalar product for symmetric functions and that this operation preserves D-finiteness.

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