Combinatorial Structures
The above operations can now be used to enumerate common combinatorial objects including trees (binary and plane), Dyck paths and cycles. A combinatorial structure is composed of atoms. For example, with trees the atoms would be the nodes. The atoms which compose the object can either be labeled or unlabeled. Unlabeled atoms are indistinguishable from each other, while labelled atoms are distinct. Therefore, for a combinatorial object consisting of labeled atoms a new object can be formed by simply swapping two or more atoms.
Read more about this topic: Enumerative Combinatorics
Famous quotes containing the word structures:
“The philosopher believes that the value of his philosophy lies in its totality, in its structure: posterity discovers it in the stones with which he built and with which other structures are subsequently built that are frequently better—and so, in the fact that that structure can be demolished and yet still possess value as material.”
—Friedrich Nietzsche (1844–1900)