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Computer Algebra Libraries for Combinatorial Structures

✍ Scribed by Philippe Flajolet; Bruno Salvy

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
652 KB
Volume
20
Category
Article
ISSN
0747-7171

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✦ Synopsis

This paper introduces the framework of decomposable combinatorial structures and their traversal algorithms. A combinatorial type is decomposable if it admits a specification in terms of unions, products, sequences, sets, and cycles, either in the labelled or in the unlabelled context. Many properties of decomposable structures are decidable. Generating function equations, counting sequences, and random generation algorithms can be compiled from specifications. Asymptotic properties can be determined automatically for a reasonably large subclass. Maple libraries that implement such decision procedures are briefly surveyed (LUO, combstruct, equivalent). In addition, libraries for manipulating holonomic sequences and functions are presented (gfun, Mgfun).

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