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Decomposition Based Generating Functions for Sequences

Published online by Cambridge University Press:  20 November 2018

D. M. Jackson  and
R. Aleliunas
D. M. Jackson
Affiliation:
University of Waterloo, Waterloo, Ontario
R. Aleliunas
Affiliation:
University of Waterloo, Waterloo, Ontario
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Numerous combinatorial enumeration problems may be reduced to equivalent problems of enumerating sequences with prescribed restrictions. For example, the expression, given by Tutte [38], for the number of planar maps may be derived (see Cori and Richard [12]) by essentially a sequence enumeration technique. The correspondence between a set of configurations which are to be enumerated and an appropriate set of sequences is often complicated. Indeed, the existence of such a correspondence has occasionally only been discovered fortuitously by observing the equality of two counting series (see, for example, Klarner [25]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 971 - 1009
Copyright
Copyright © Canadian Mathematical Society 1977

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