The kernel method and systems of functional equations with several conditions

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摘要

We generalize the kernel method to equation systems in which the number of unknowns is allowed to exceed the number of equations. With this generalization, we derive the generating functions for several kinds of sequences and generating trees whose recursions are dependent on the parity of the indices.

论文关键词：65Q05,05A15,Kernel method,Generating functions,Sequences with two indices,Generating trees

论文评审过程：Received 15 January 2009, Revised 26 February 2010, Available online 10 August 2010.

论文官网地址：https://doi.org/10.1016/j.cam.2010.08.004