Constant time generation of set partitions

被引：12

作者：

Kawano, S ^{[1
]}

Nakano, S ^{[1
]}

机构：

[1] Gunma Univ, Dept Comp Sci, Kiryu, Gumma 3768515, Japan

来源：

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES | 2005年 / E88A卷 / 04期

关键词：

algorithm; enumeration; the Stirling number of the second kind; the Bell number; Gray code;

D O I：

10.1093/ietfec/e88-a.4.930

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：930 / 934

页数：5

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