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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 the Pólya 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 wikiPageLength "26279".
- Cycle_index wikiPageOutDegree "51".
- Cycle_index wikiPageRevisionID "653177144".
- Cycle_index wikiPageWikiLink Abstract_group.
- Cycle_index wikiPageWikiLink Alternating_group.
- Cycle_index wikiPageWikiLink Analysis_of_algorithms.
- Cycle_index wikiPageWikiLink Analytic_combinatorics.
- Cycle_index wikiPageWikiLink Bell_polynomial.
- Cycle_index wikiPageWikiLink Bell_polynomials.
- Cycle_index wikiPageWikiLink Bijection.
- Cycle_index wikiPageWikiLink Bijective_mapping.
- Cycle_index wikiPageWikiLink Burnsides_lemma.
- Cycle_index wikiPageWikiLink Category:Combinatorics.
- Cycle_index wikiPageWikiLink Category:Enumerative_combinatorics.
- Cycle_index wikiPageWikiLink Cayleys_theorem.
- Cycle_index wikiPageWikiLink Combinatorial_enumeration.
- Cycle_index wikiPageWikiLink Combinatorial_mathematics.
- Cycle_index wikiPageWikiLink Combinatorial_species.
- Cycle_index wikiPageWikiLink Combinatorics.
- Cycle_index wikiPageWikiLink Complete_digraph.
- Cycle_index wikiPageWikiLink Complete_graph.
- Cycle_index wikiPageWikiLink Cyclic_group.
- Cycle_index wikiPageWikiLink Cyclic_permutation.
- Cycle_index wikiPageWikiLink Dihedral_group.
- Cycle_index wikiPageWikiLink Enumerative_combinatorics.
- Cycle_index wikiPageWikiLink Equilateral_triangle.
- Cycle_index wikiPageWikiLink Euclidean_plane.
- Cycle_index wikiPageWikiLink Eulers_totient_function.
- Cycle_index wikiPageWikiLink Exponential_generating_function.
- Cycle_index wikiPageWikiLink Finite_set.
- Cycle_index wikiPageWikiLink Free_variables_and_bound_variables.
- Cycle_index wikiPageWikiLink Generating_function.
- Cycle_index wikiPageWikiLink Glossary_of_graph_theory.
- Cycle_index wikiPageWikiLink Group_(mathematics).
- Cycle_index wikiPageWikiLink Group_action.
- Cycle_index wikiPageWikiLink Group_homomorphism.
- Cycle_index wikiPageWikiLink Kernel_(algebra).
- Cycle_index wikiPageWikiLink Line_graph.
- Cycle_index wikiPageWikiLink Monomial.
- Cycle_index wikiPageWikiLink Orbit_(group_theory).
- Cycle_index wikiPageWikiLink Ordinary_generating_function.
- Cycle_index wikiPageWikiLink Partition_of_a_set.
- Cycle_index wikiPageWikiLink Permutation.
- Cycle_index wikiPageWikiLink Permutation_group.
- Cycle_index wikiPageWikiLink Pxc3xb3lyas_enumeration_theorem.
- Cycle_index wikiPageWikiLink Pólya_enumeration_theorem.
- Cycle_index wikiPageWikiLink Random_permutation_statistics.
- Cycle_index wikiPageWikiLink Rotational_symmetries.
- Cycle_index wikiPageWikiLink Rotational_symmetry.
- Cycle_index wikiPageWikiLink Square.
- Cycle_index wikiPageWikiLink Square_(geometry).
- Cycle_index wikiPageWikiLink Subgroup.
- Cycle_index wikiPageWikiLink Symbolic_combinatorics.
- Cycle_index wikiPageWikiLink Symmetric_group.
- Cycle_index wikiPageWikiLink Tetrahedral_symmetry.
- Cycle_index wikiPageWikiLink Two-dimensional_space.
- Cycle_index wikiPageWikiLink File:Face_colored_cube.png.
- Cycle_index wikiPageWikiLinkText "Cycle index of the dihedral group".
- Cycle_index wikiPageWikiLinkText "Cycle index".
- Cycle_index wikiPageWikiLinkText "cycle index".
- Cycle_index wikiPageWikiLinkText "here".
- Cycle_index hasPhotoCollection Cycle_index.
- Cycle_index wikiPageUsesTemplate Template:Citation.
- Cycle_index wikiPageUsesTemplate Template:Cite_journal.
- Cycle_index wikiPageUsesTemplate Template:Reflist.
- Cycle_index subject Category:Combinatorics.
- Cycle_index subject Category:Enumerative_combinatorics.
- Cycle_index hypernym Polynomial.
- Cycle_index type Article.
- Cycle_index type Article.
- Cycle_index type Combinatoric.
- Cycle_index type Field.
- 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.".
- Cycle_index label "Cycle index".
- Cycle_index sameAs Zyklenzeiger.
- Cycle_index sameAs Indicateur_de_cycles.
- Cycle_index sameAs m.0cj_9x.
- Cycle_index sameAs Cykelindex.
- Cycle_index sameAs வரிசைமாற்றக்_குலத்தின்_சுழற்_குறியீடு.
- Cycle_index sameAs Q245446.
- Cycle_index sameAs Q245446.
- Cycle_index wasDerivedFrom Cycle_index?oldid=653177144.
- Cycle_index isPrimaryTopicOf Cycle_index.