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m →Labelled structures: Graph (mathematics) is now a disambiguation link; please fix., replaced: labelled graph{{dn|date=January 2016}} → labelled graph using AWB |
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==Labelled structures==
An object is ''weakly labelled'' if each of its atoms has a nonnegative integer label, and each of these labels is distinct. An object is (''strongly'' or ''well'') ''labelled'', if furthermore, these labels comprise the consecutive integers <math>[1 \ldots n]</math>. ''Note: some combinatorial classes are best specified as labelled structures or unlabelled structures, but some readily admit both specifications.'' A good example of labelled structures is the class of [[Graph (discrete mathematics)|labelled graph]]
With labelled structures, an [[exponential generating function]] (EGF) is used. The EGF of a sequence <math>A_{n}</math> is defined as
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