Symbolic method (combinatorics): Difference between revisions

Revision as of 00:08, 16 March 2018

Revision as of 00:14, 16 March 2018

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\frac{1}{2} \log \frac{1+g(z)}{1-g(z)}.</math>

=== The multiset/set operator <math>\mathfrakoperatorname{MMSET}/\mathfrakoperatorname{PSET}</math> ===

The series is

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\sum_{n\ge 0} \frac{g(z)^n}{n!} = \exp g(z).</math>

In the labelled case we denote the operator by <math>\mathfrakoperatorname{PSET}</math>, and in the unlabelled case, by <math>\mathfrakoperatorname{MMSET}</math>. This is because in the labeled case there are no multisets (the labels distinguish the constituents of a compound combinatorial class) whereas in the unlabeled case there are multisets and sets, with the latter being given by

:<math> F(z) = \exp \left( \sum_{l\ge 1} (-1)^{l-1} \frac{f(z^l)}{l} \right).</math>

==Procedure==