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WhackTheWiki (talk | contribs) m →References: Add Micha Hofri's book (cited in Flajolet and Sedgewick) to list of references. |
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===Product===
For labelled structures, we must use a different definition for product than for unlabelled structures. In fact, if we simply used the cartesian product, the resulting structures would not even be well labelled. Instead, we use the so-called ''labelled product'', denoted <math>\mathcal{A} \star \mathcal{B}.</math>
For a pair <math>\beta \in \mathcal{B}</math> and <math>\gamma \in \mathcal{C}</math>, we wish to combine the two structures into a single structure. In order for the result to be well labelled, this requires some relabelling of the atoms in <math>\beta</math> and <math>\gamma</math>. We will restrict our attention to relabellings that are consistent with the order of the original labels. Note that there are still multiple ways to do the relabelling; thus, each pair of members determines not a single member in the product, but a set of new members. The details of this construction are found on the page of the [[Labelled enumeration theorem]].
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