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	Kernel method and system of functional equations
	Mansour, Toufik ; Song, Chunwei
	2009
关键词	Kernel method Generating functions Descents Signed permutations RECURRENCE RELATIONS DESCENT NUMBERS MAJOR INDEXES STATISTICS TREES
英文摘要	Introduced by Knuth and subsequently developed by Banderier et al., Prodinger, and others, the kernel method is a powerful too] for solving power series equations ill the form of F(z, t) = A(z, t)F(z(0), t) + B(z, t) and several variations. Recently, Hou and Mansour [Q.-H. Hou, T. Mansour, Kernel Method and Linear Recurrence System, J. Comput. Appl. Math. (2007), (in press).] presented a systematic method to solve equation systems of two variables F(z, t) = A(z, t)F(z(0), t) + B(z, t), where A is a matrix, and F and B are vectors of rational functions in z and I. In this paper we generalize this method to another type of rational function matrices, i.e., systems of functional equations. Since the types of equation systems we are interested ill arise frequently in various enumeration questions via generating functions, our tool is quite useful in solving enumeration problems. To illustrate this, we provide several applications, namely the recurrence relations with two indices, and Counting descents in signed permutations. (C) 2008 Elsevier B.V. All rights reserved.; Mathematics, Applied; SCI(E); EI; 2; ARTICLE; 1; 133-139; 224
语种	英语
出处	EI ; SCI
出版者	计算与应用数学杂志
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/246556]
专题	数学科学学院
推荐引用方式 GB/T 7714	Mansour, Toufik,Song, Chunwei. Kernel method and system of functional equations. 2009-01-01.

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