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- Cycle_index abstract "In combinatorial mathematics a cycle index is a polynomial in several variables which is structured in such a way that information about how a group of permutations acts on a set can be simply read off from the coefficients and exponents. This compact way of storing information in an algebraic form is frequently used in combinatorial enumeration. Each permutation π of a finite set of objects partitions that set into cycles; the cycle index monomial of π is a monomial in variables a1, a2, … that describes the type of this partition (the cycle type of π): the exponent of ai is the number of cycles of π of size i. The cycle index polynomial of a permutation group is the average of the cycle index monomials of its elements. The phrase cycle indicator is also sometimes used in place of cycle index.Knowing the cycle index polynomial of a permutation group, one can enumerate equivalence classes due to the group's action. This is the main ingredient in Pólya's enumeration theorem. Performing formal algebraic and differential operations on these polynomials and then interpreting the results combinatorially lies at the core of species theory.".
- Cycle_index wikiPageExternalLink collier.pdf.
- Cycle_index wikiPageExternalLink linaffproj.html.
- Cycle_index wikiPageID "4720804".
- Cycle_index wikiPageRevisionID "590679555".
- Cycle_index hasPhotoCollection Cycle_index.
- Cycle_index subject Category:Combinatorics.
- Cycle_index subject Category:Enumerative_combinatorics.
- Cycle_index comment "In combinatorial mathematics a cycle index is a polynomial in several variables which is structured in such a way that information about how a group of permutations acts on a set can be simply read off from the coefficients and exponents. This compact way of storing information in an algebraic form is frequently used in combinatorial enumeration.".
- Cycle_index label "Cycle index".
- Cycle_index label "Indicateur de cycles".
- Cycle_index label "Zyklenzeiger".
- Cycle_index sameAs Zyklenzeiger.
- Cycle_index sameAs Indicateur_de_cycles.
- Cycle_index sameAs m.0cj_9x.
- Cycle_index sameAs Q245446.
- Cycle_index sameAs Q245446.
- Cycle_index wasDerivedFrom Cycle_index?oldid=590679555.
- Cycle_index isPrimaryTopicOf Cycle_index.