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In mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as a concatenation of elements drawn from the subsets. The Chen–Fox–Lyndon theorem states that the Lyndon words furnish a factorisation. The Schützenberger theorem relates the definition in terms of a multiplicative property to an additive property. Let A* be the free monoid on an alphabet A. Let Xi be a sequence of subsets of A* indexed by a totally ordered index set I. A factorisation of a word w in A* is an expression

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Communication100033020 yago:Language106282651 yago:WikicatFormalLanguages
rdfs:label	Faktorisasi monoid (in) Monoid factorisation (en)
rdfs:comment	In mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as a concatenation of elements drawn from the subsets. The Chen–Fox–Lyndon theorem states that the Lyndon words furnish a factorisation. The Schützenberger theorem relates the definition in terms of a multiplicative property to an additive property. Let A* be the free monoid on an alphabet A. Let Xi be a sequence of subsets of A* indexed by a totally ordered index set I. A factorisation of a word w in A* is an expression (en) Dalam matematika, faktorisasi dari monoid bebas adalah urutan himpunan bagian kata dengan properti bahwa setiap kata dalam monoid bebas dapat ditulis sebagai rangkaian elemen yang diambil dari himpunan bagian tersebut. Teorema Chen–Fox–Lyndon menyatakan bahwa memberikan sebuah faktorisasi. Teorema Schützenberger menghubungkan definisi dalam hal sifat perkalian dengan sifat aditif. Misalkan adalah monoid bebas pada huruf . Misalkan adalah urutan himpunan bagian dari yang diindeks oleh himpunan indeks . Faktorisasi sebuah kata pada adalah ekspresi (in)
dcterms:subject	Formal languages
Wikipage page ID	37206260 (xsd:integer)
Wikipage revision ID	1071556751 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Index set Mathematics Gian-Carlo Rota Monoid Lexicographic order Linear time Hall word Totally ordered set Disjoint sets Sesquipower Jean-Éric Pin Formal languages Free monoid If and only if Ralph Fox Lyndon word Roger Lyndon Subset Hall set Singleton set Marcel Schützenberger
sameAs	Monoid factorisation Monoid factorisation Monoid factorisation Monoid factorisation Monoid factorisation
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Clarify dbt:Reflist
date	October 2020 (en)
reason	What, exactly, is the "additive property", here? What makes this additive? I have a vague glimmer of what it might be,but this statement is imprecise. (en) What, exactly is meant by "meet", here? I assume that it means that the intersection of C and M_i is non-empty for one and only one i? Right? I dislike having to guess; I sometimes guess incorrectly. (en) What does "required form" mean here? I guess I should assume the "required form" is the product in descending order, given previously, right? The wording is awkward. (en)
has abstract	In mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as a concatenation of elements drawn from the subsets. The Chen–Fox–Lyndon theorem states that the Lyndon words furnish a factorisation. The Schützenberger theorem relates the definition in terms of a multiplicative property to an additive property. Let A* be the free monoid on an alphabet A. Let Xi be a sequence of subsets of A* indexed by a totally ordered index set I. A factorisation of a word w in A* is an expression with and . Some authors reverse the order of the inequalities. (en) Dalam matematika, faktorisasi dari monoid bebas adalah urutan himpunan bagian kata dengan properti bahwa setiap kata dalam monoid bebas dapat ditulis sebagai rangkaian elemen yang diambil dari himpunan bagian tersebut. Teorema Chen–Fox–Lyndon menyatakan bahwa memberikan sebuah faktorisasi. Teorema Schützenberger menghubungkan definisi dalam hal sifat perkalian dengan sifat aditif. Misalkan adalah monoid bebas pada huruf . Misalkan adalah urutan himpunan bagian dari yang diindeks oleh himpunan indeks . Faktorisasi sebuah kata pada adalah ekspresi dengan dan . Beberapa penulis membalik urutan ketidaksetaraan. (in)
prov:wasDerivedFrom	wikipedia-en:Monoid_factorisation?oldid=1071556751&ns=0
page length (characters) of wiki page	4874 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Monoid_factorisation
is Link from a Wikipage to another Wikipage of	List of abstract algebra topics Commutator collecting process Chen–Fox–Lyndon theorem Hall word Sesquipower Factorization Chen-Fox-Lyndon theorem Fermat's factorization method Schützenberger theorem
is Wikipage redirect of	Chen–Fox–Lyndon theorem Chen-Fox-Lyndon theorem Schützenberger theorem
is foaf:primaryTopic of	wikipedia-en:Monoid_factorisation

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