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 . 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 labelled graphs.
With labelled structures, an exponential generating function (EGF) is used. The EGF of a sequence is defined as
Read more about this topic: Symbolic Combinatorics
Famous quotes containing the words labelled and/or structures:
“The experience and behaviour that gets labelled schizophrenic is a special strategy that a person invents in order to live in an unlivable situation.”
—R.D. (Ronald David)
“The American who has been confined, in his own country, to the sight of buildings designed after foreign models, is surprised on entering York Minster or St. Peter’s at Rome, by the feeling that these structures are imitations also,—faint copies of an invisible archetype.”
—Ralph Waldo Emerson (1803–1882)