Journal of Integer Sequences, Vol. 10 (2007), Article 07.5.5

Automatic Enumeration of Regular Objects

Marni Mishna
Department of Mathematics
Simon Fraser University
8888 University Drive
Burnaby, BC V5A 1S6


We describe a framework for systematic enumeration of families combinatorial structures that possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These differential equations are then used to determine the initial terms in the counting sequence and for asymptotic analysis. The key tool is the scalar product for symmetric functions.

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(Concerned with sequences A000986 A001147 A001205 A002135 A002137 A002829 A005814 A025035 A108243 A108246 A110039 A110040 A110041 A110100 A110101 A110102 and A110103 .)

Received October 23 2006; revised version received May 10 2007. Published in Journal of Integer Sequences May 10 2007.

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