Symbolic method (combinatorics): Difference between revisions

Revision as of 20:58, 23 June 2013

Revision as of 07:33, 23 July 2013

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:<math>G(z) = \frac{z}{1 - G(z)}</math>

we solve for G(z) by multiplying <math>1 - G(z)</math> to get

<math>G(z) - G(z)^2 = z</math>

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:<math>\alpha \star \beta = \{(\alpha',\beta'): (\alpha',\beta') \mbox{ is well-labelled, } \rho(\alpha') = \alpha, \rho(\beta') = \beta \}.</math>

Finally, the labelled product of two classes <math>\mathcal{A}</math> and <math>\mathcal{B}</math> is

:<math>\mathcal{A} \star \mathcal{B} = \bigcup_{\alpha \in \mathcal{A}, \beta \in \mathcal{B}} (\alpha \star \beta).</math>

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==References==

* François Bergeron, Gilbert Labelle, Pierre Leroux, ''Théorie des espèces et combinatoire des structures arborescentes'', LaCIM, Montréal (1994). English version: ''Combinatorial Species and Tree-like Structures'', Cambridge University Press (1998).

* Philippe Flajolet and Robert Sedgewick, ''Analytic Combinatorics'', Cambridge University Press (2009). (available online: http://algo.inria.fr/flajolet/Publications/book.pdf‎pdf)

[[Category:Combinatorics]]