Computer Algebra Libraries for Combinatorial Structures

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 properti...

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Vydáno v:Journal of symbolic computation Ročník 20; číslo 5; s. 653 - 671
Hlavní autoři: Flajolet, Philippe, Salvy, Bruno
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.11.1995
ISSN:0747-7171, 1095-855X
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Abstract 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).
AbstractList 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).
Author Flajolet, Philippe
Salvy, Bruno
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CitedBy_id crossref_primary_10_1016_j_tcs_2005_08_028
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crossref_primary_10_1145_2430532_2364515
crossref_primary_10_1002_rsa_10025
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crossref_primary_10_1145_2858965_2814323
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