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	Enumerating set partitions according to the number of descents of size d or more
	Mansour, Toufik ; Shattuck, Mark ; Song, Chunwei
	2012
关键词	Set partitions descents partition statistic combinatorial proof
英文摘要	Let P (n, k) denote the set of partitions of {1, 2, ... , n} having exactly k blocks. In this paper, we find the generating function which counts the members of P (n, k) according to the number of descents of size d or more, where d >= 1 is fixed. An explicit expression in terms of Stirling numbers of the second kind may be given for the total number of such descents in all the members of P (n, k). We also compute the generating function for the statistics recording the number of ascents of size d or more and show that it has the same distribution on P (n, k) as the prior statistics for descents when d >= 2, by both algebraic and combinatorial arguments.; Mathematics; SCI(E); EI; 0; ARTICLE; 4; 507-517; 122
语种	英语
出处	EI ; SCI
出版者	proceedings of the indian academy of sciences mathematical sciences
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/230035]
专题	数学科学学院
推荐引用方式 GB/T 7714	Mansour, Toufik,Shattuck, Mark,Song, Chunwei. Enumerating set partitions according to the number of descents of size d or more. 2012-01-01.

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