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Refined Stirling Numbers: Enumeration of Special Sets of Permutations and Set-Partitions

✍ Scribed by J. Katriel

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 110 KB
Volume: 99
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2002.3259

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✦ Synopsis

The refined Stirling numbers of the first kind

specify the number of permutations of n indices possessing m i cycles whose lengths modulo k are congruent to i; i ¼ 0; 1; 2; . . . ; k À 1: The refined Stirling numbers of the second kind

are similarly defined in terms of set-partitions and the cardinalities of their disjoint blocks. Generating functions for these two types of refined Stirling numbers are derived using the Fa" a a di Bruno formula. These generating functions allow the derivation of recurrence relations for both types of refined Stirling numbers. # 2002

Elsevier Science (USA)

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