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Algorithm 29 efficient algorithms for doubly and multiply restricted partitions

Effiziente Algorithmen für zweifach oder mehrfach beschränkte Partitionen

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Abstract

An account is given of algorithms for constructing partitions of an integer into a specified number of parts (with or without the requirement that the parts be distinct). The allowed parts may form a segment or a more general prescribed set of integers. Two ALGOL procedures are given, and some computational results are discussed.

Zusammenfassung

Es werden Algorithmen beschrieben zur Konstruktion der Partitionen einer ganzen Zahl in eine vorgeschriebene Anzahl von (verschiedenen oder nicht notwendig verschiedenen) Teilen. Die zugelassenen Teile können aus einem ganzzahligen Intervall oder einer allgemeineren Menge von ganzen Zahlen gewählt werden. Zwei ALGOL-Prozeduren werden angegeben, und einige Resultate diskutiert.

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References

  1. Berge, C.: Principles of Combinatorics. Academic Press 1971.

  2. James, K. R., Riha, W.: Algorithm for Generating Graphs of a Given Partition. Computing16, 153–161 (1976).

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  3. James, K. R., Riha, W.: The Production of Trees and Rooted Trees of Order ≤15, Classified According to Partition. Report No. 47, Centre for computer Studies, University of Leeds, 1974.

  4. McKay, J. K. S.: Algorithm 263, Partition Generator. Comm. of the ACM8 (1965).

  5. White, J. S.: Algorithm 374, Restricted Partition Generator. Comm. of the ACM13 (1970).

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Riha, W., James, K.R. Algorithm 29 efficient algorithms for doubly and multiply restricted partitions. Computing 16, 163–168 (1976). https://doi.org/10.1007/BF02241987

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  • DOI: https://doi.org/10.1007/BF02241987

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