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- W2031970511 abstract "The refined Stirling numbers of the first kindnm0m1 ··· mk−1 specify the number of permutations of n indices possessing mi cycles whose lengths modulo k are congruent to i, i=0,1,2,…,k−1. The refined Stirling numbers of the second kindnm0m1 ··· mk−1 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 Faà di Bruno formula. These generating functions allow the derivation of recurrence relations for both types of refined Stirling numbers." @default.
- W2031970511 created "2016-06-24" @default.
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- W2031970511 date "2002-07-01" @default.
- W2031970511 modified "2023-10-04" @default.
- W2031970511 title "Refined Stirling Numbers: Enumeration of Special Sets of Permutations and Set-Partitions" @default.
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- W2031970511 doi "https://doi.org/10.1006/jcta.2002.3259" @default.
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