Symbolic method (combinatorics): Difference between revisions

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===Sequence===
The ''sequence construction'', denoted by <math>\mathcal{A} = \mathfrak{G}\{\mathcal{B}\}</math> is defined as
 
:<math>\mathfrak{G}\{\mathcal{B}\} = \mathcal{E} + \mathcal{B} + (\mathcal{B} \times \mathcal{B}) + (\mathcal{B} \times \mathcal{B} \times \mathcal{B}) + \cdots.</math>
 
In other words, a sequence is the neutral element, or an element of <math>\mathcal{B}</math>, or an ordered pair, ordered triple, etc. This leads to the relation
 
:<math>A(z) = 1 + B(z) + B(z)^{2} + B(z)^{3} + \cdots = \frac{1}{1 - B(z)}.</math>
 
===Set===