Constant Time Generation of Set Partitions

Shin-ichiro KAWANO; Shin-ichi NAKANO

doi:10.1093/ietfec/e88-a.4.930

Constant Time Generation of Set Partitions

Shin-ichiro KAWANO, Shin-ichi NAKANO

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In this paper we give a simple algorithm to generate all partitions of {1,2,,n} into k non-empty subsets. The number of such partitions is known as the Stirling number of the second kind. The algorithm generates each partition in constant time without repetition. By choosing k = 1,2,,n we can also generate all partitions of {1,2,,n} into subsets. The number of such partitions is known as the Bell number.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E88-A No.4 pp.930-934

Publication Date: 2005/04/01

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DOI: 10.1093/ietfec/e88-a.4.930

Type of Manuscript: Special Section PAPER (Special Section on Selected Papers from the 17th Workshop on Circuits and Systems in Karuizawa)

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Shin-ichiro KAWANO, Shin-ichi NAKANO, "Constant Time Generation of Set Partitions" in IEICE TRANSACTIONS on Fundamentals, vol. E88-A, no. 4, pp. 930-934, April 2005, doi: 10.1093/ietfec/e88-a.4.930.
Abstract: In this paper we give a simple algorithm to generate all partitions of {1,2,,n} into k non-empty subsets. The number of such partitions is known as the Stirling number of the second kind. The algorithm generates each partition in constant time without repetition. By choosing k = 1,2,,n we can also generate all partitions of {1,2,,n} into subsets. The number of such partitions is known as the Bell number.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e88-a.4.930/_p

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@ARTICLE{e88-a_4_930,
author={Shin-ichiro KAWANO, Shin-ichi NAKANO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Constant Time Generation of Set Partitions},
year={2005},
volume={E88-A},
number={4},
pages={930-934},
abstract={In this paper we give a simple algorithm to generate all partitions of {1,2,,n} into k non-empty subsets. The number of such partitions is known as the Stirling number of the second kind. The algorithm generates each partition in constant time without repetition. By choosing k = 1,2,,n we can also generate all partitions of {1,2,,n} into subsets. The number of such partitions is known as the Bell number.},
keywords={},
doi={10.1093/ietfec/e88-a.4.930},
ISSN={},
month={April},}

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TY - JOUR
TI - Constant Time Generation of Set Partitions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 930
EP - 934
AU - Shin-ichiro KAWANO
AU - Shin-ichi NAKANO
PY - 2005
DO - 10.1093/ietfec/e88-a.4.930
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E88-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2005
AB - In this paper we give a simple algorithm to generate all partitions of {1,2,,n} into k non-empty subsets. The number of such partitions is known as the Stirling number of the second kind. The algorithm generates each partition in constant time without repetition. By choosing k = 1,2,,n we can also generate all partitions of {1,2,,n} into subsets. The number of such partitions is known as the Bell number.
ER -