Symbolic method (combinatorics): Difference between revisions

Revision as of 07:03, 8 December 2021

Revision as of 14:11, 10 August 2023

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:<math>\mathcal{P} = \operatorname{MSET}\{\mathcal{I}\}. </math>

The OGF of <math>\mathcal{P}</math> is

:<math>P(z) = \exp \left ( I(z) + \frac{1}{2} I(z^{2}) + \frac{1}{3} I(z^{3}) + \cdots \right ). </math>

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===Specification and specifiable classes===

The elementary constructions mentioned above allow to define the notion of ''specification''. Those specificationspecifications allow to use a set of recursive equations, with multiple combinatorial classes.

Formally, a specification for a set of combinatorial classes <math>(\mathcal A_1,\dots,\mathcal A_r)</math> is a set of <math>r</math> equations <math>\mathcal A_i=\Phi_i(\mathcal A_1,\dots,\mathcal A_r)</math>, where <math>\Phi_i</math> is an expression, whose atoms are <math>\mathcal E,\mathcal Z</math> and the <math>\mathcal A_i</math>'s, and whose operators are the elementary constructions listed above.