European Journal of Combinatorics
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Descent Numbers and Major Indices for the Hyperoctahedral Group
Advances in Applied Mathematics
Generating functions for generating trees
Discrete Mathematics
Statistics on wreath products, perfect matchings, and signed words
European Journal of Combinatorics - Special issue on combinatorics and representation theory
Three Hoppy path problems and ternary paths
Discrete Applied Mathematics
Kernel method and linear recurrence system
Journal of Computational and Applied Mathematics
The kernel method and systems of functional equations with several conditions
Journal of Computational and Applied Mathematics
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Introduced by Knuth and subsequently developed by Banderier et al., Prodinger, and others, the kernel method is a powerful tool for solving power series equations in 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 t. 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 in 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.