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- Labelled_enumeration_theorem abstract "In combinatorial mathematics, the labelled enumeration theorem is the counterpart of the Pólya enumeration theorem for the labelled case, where we have a set of labelled objects given by an exponential generating function (EGF) g(z) which are being distributed into n slots and a permutation group G which permutes the slots, thus creating equivalence classes of configurations. There is a special re-labelling operation that re-labels the objects in the slots, assigning labels from 1 to k, where k is the total number of nodes, i.e. the sum of the number of nodes of the individual objects. The EGF of the number of different configurations under this re-labelling process is given byIn particular, if G is the symmetric group of order n (hence, |G| = n!), the functions f_n(z) can be further combined into a single generating function:which is exponential w.r.t. the variable z and ordinary w.r.t. the variable t.".
- Labelled_enumeration_theorem thumbnail RelabelCycles.png?width=300.
- Labelled_enumeration_theorem wikiPageID "34871920".
- Labelled_enumeration_theorem wikiPageRevisionID "595154801".
- Labelled_enumeration_theorem hasPhotoCollection Labelled_enumeration_theorem.
- Labelled_enumeration_theorem subject Category:Articles_containing_proofs.
- Labelled_enumeration_theorem subject Category:Enumerative_combinatorics.
- Labelled_enumeration_theorem subject Category:Mathematical_theorems.
- Labelled_enumeration_theorem type Abstraction100002137.
- Labelled_enumeration_theorem type Communication100033020.
- Labelled_enumeration_theorem type MathematicalTheorems.
- Labelled_enumeration_theorem type Message106598915.
- Labelled_enumeration_theorem type Proposition106750804.
- Labelled_enumeration_theorem type Statement106722453.
- Labelled_enumeration_theorem type Theorem106752293.
- Labelled_enumeration_theorem comment "In combinatorial mathematics, the labelled enumeration theorem is the counterpart of the Pólya enumeration theorem for the labelled case, where we have a set of labelled objects given by an exponential generating function (EGF) g(z) which are being distributed into n slots and a permutation group G which permutes the slots, thus creating equivalence classes of configurations.".
- Labelled_enumeration_theorem label "Labelled enumeration theorem".
- Labelled_enumeration_theorem sameAs m.0cv8cv.
- Labelled_enumeration_theorem sameAs Q6466909.
- Labelled_enumeration_theorem sameAs Q6466909.
- Labelled_enumeration_theorem sameAs Labelled_enumeration_theorem.
- Labelled_enumeration_theorem wasDerivedFrom Labelled_enumeration_theorem?oldid=595154801.
- Labelled_enumeration_theorem depiction RelabelCycles.png.
- Labelled_enumeration_theorem isPrimaryTopicOf Labelled_enumeration_theorem.
