The kernel method and systems of functional equations with several conditions

Authors:
Qing-Hu Hou;Toufik Mansour
Affiliations:
Center for Combinatorics, LPMC-TJKLC, Nankai University, 300071 Tianjin, PR China;Department of Mathematics, University of Haifa, 31905 Haifa, Israel
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

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.