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A combinatorial structure is a discrete mathematical object specified by underlying elements and rules organizing them. A graph equips a set of vertices with edges; a permutation orders labels; a set partition groups them into nonempty subsets. Counting requires an explicit equality convention. Two labelled combinatorial structures may differ only by their labels, whereas an unlabelled combinatorial structure identifies objects related by an appropriate isomorphism. Thus there are three labelled two-element subsets of a three-element set, but only one abstract two-element set up to bijection.