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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| Published in: | Journal of symbolic computation Vol. 20; no. 5; pp. 653 - 671 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Ltd
01.11.1995
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| ISSN: | 0747-7171, 1095-855X |
| Online Access: | Get full text |
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| Summary: | 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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| ISSN: | 0747-7171 1095-855X |
| DOI: | 10.1006/jsco.1995.1070 |