About: Necklace (combinatorics)

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In combinatorics, a k-ary necklace of length n is an equivalence class of n-character strings over an alphabet of size k, taking all rotations as equivalent. It represents a structure with n circularly connected beads which have k available colors. Formally, one may represent a necklace as an orbit of the cyclic group acting on n-character strings over an alphabet of size k, and a bracelet as an orbit of the dihedral group. One can count these orbits, and thus necklaces and bracelets, using Pólya's enumeration theorem.

Attributes	Values
rdfs:label	Necklace (combinatorics) (en)
rdfs:comment	In combinatorics, a k-ary necklace of length n is an equivalence class of n-character strings over an alphabet of size k, taking all rotations as equivalent. It represents a structure with n circularly connected beads which have k available colors. Formally, one may represent a necklace as an orbit of the cyclic group acting on n-character strings over an alphabet of size k, and a bracelet as an orbit of the dihedral group. One can count these orbits, and thus necklaces and bracelets, using Pólya's enumeration theorem. (en)
sameAs	Necklace (combinatorics)
dbp:wikiPageUsesTemplate	dbt:Main dbt:MathWorld dbt:OEIS dbt:Reflist dbt:Sfrac
Subject	Combinatorics on words Enumerative combinatorics
gold:hypernym	Class
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Necklace_(combinatorics)?oldid=1066490505&ns=0
Wikipage page ID	6226587 (xsd:integer)
page length (characters) of wiki page	7147 (xsd:nonNegativeInteger)
Wikipage revision ID	1066490505 (xsd:integer)
Link from a Wikipage to another Wikipage	Forte number Möbius function Möbius inversion formula Proofs of Fermat's little theorem Alphabet (formal languages) Atonality Binomial coefficient Combinatorics on words Dihedral group Pólya enumeration theorem Circular shift Cyclic group Combinatorics Equivalence class Permutation Group action Inversion (discrete mathematics) Euler's totient function Stirling numbers of the second kind String (computer science) Lyndon word Multiset Necklace polynomial Necklace problem Necklace splitting problem Enumerative combinatorics
has abstract	In combinatorics, a k-ary necklace of length n is an equivalence class of n-character strings over an alphabet of size k, taking all rotations as equivalent. It represents a structure with n circularly connected beads which have k available colors. A k-ary bracelet, also referred to as a turnover (or free) necklace, is a necklace such that strings may also be equivalent under reflection. That is, given two strings, if each is the reverse of the other, they belong to the same equivalence class. For this reason, a necklace might also be called a fixed necklace to distinguish it from a turnover necklace. Formally, one may represent a necklace as an orbit of the cyclic group acting on n-character strings over an alphabet of size k, and a bracelet as an orbit of the dihedral group. One can count these orbits, and thus necklaces and bracelets, using Pólya's enumeration theorem. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Necklace_(combinatorics)
is Wikipage redirect of	Bracelet (combinatorics) Bracelet (mathematics) Necklace (mathematics)
is Link from a Wikipage to another Wikipage of	Forte number 208 (number) 232 (number) 246 (number) Anhemitonic scale Augmented sixth chord Bracelet (disambiguation) Double counting (proof technique) Circular shift Cycle Combinatorics on words Edgar Gilbert Index of combinatorics articles Factorization of polynomials over finite fields Monic polynomial Lyndon word Multiplication (music) Necklace (disambiguation) Necklace polynomial Necklace problem Necklace splitting problem Bracelet (combinatorics) Bracelet (mathematics) Necklace (mathematics)
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Necklace_(combinatorics)

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