About: Incidence algebra

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In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for every locally finite partially ordered setand commutative ring with unity. Subalgebras called reduced incidence algebras give a natural construction of various types of generating functions used in combinatorics and number theory.

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rdfs:label	Inzidenzalgebra (de) Álgebra de incidencia (es) Incidence algebra (en) Algebra di incidenza (it) 근접 대수 (ko) 隣接代数 (順序理論) (ja) Álgebra de incidência (pt)
rdfs:comment	Die Inzidenzalgebra einer Halbordnung wurde 1964 von Gian-Carlo Rota zur Untersuchung kombinatorischer Sachverhalte eingeführt. (de) In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for every locally finite partially ordered setand commutative ring with unity. Subalgebras called reduced incidence algebras give a natural construction of various types of generating functions used in combinatorics and number theory. (en) ( 이 문서는 순서론과 조합론에서, 결합 관계(영어: incidence)를 추상화한 대수적 구조에 관한 것입니다. 결합법칙(영어: associativity)을 만족시키는 일반적인 대수에 대해서는 대수 (환론) 문서를 참고하십시오.) 순서론에서 근접 대수(近接代數, 영어: incidence algebra)는 부분 순서 집합에 대하여 정의된, 일반화 뫼비우스 반전 공식이 성립하는 단위 결합 대수이다. (ko) 数学の順序集合論において隣接代数（りんせつだいすう、英: incidence algebra）または接合環（せつごうかん）とは、任意の局所有限な半順序集合と単位元を持つ可換環に対して定義される結合多元環である。局所有界半順序集合の接続代数は、1964年のジャン・カルロ・ロタ(Gian-Carlo Rota)による論文に始まり、多くの組合せ論研究者により発展した。 (ja) In matematica, e più specificamente in teoria degli ordini, per algebra di incidenza si intende un'algebra associativa definita opportunamente per un qualsiasi insieme parzialmente ordinato localmente finito e un qualsiasi anello commutativo (dotato di unità). (it) Dados um conjunto parcialmente ordenado localmente finito X e um anel comutativo com unidade R, a álgebra de incidência de X sobre R (denotada por I(X,R)) é definida como sendo o conjunto de todas as aplicações f:X×X→R satisfazendo f(u,v)=0 se u não for menor do que v ou igual a v. A multiplicação por escalares de R e a adição dessa álgebra são usuais, a saber: (f+g)(u,v)=f(u,v)+g(u,v) e (λf)(u,v)=λ(f(u,v), para quaisquer u, v pertencentes a X e qualquer λ pertencente a R. A multiplicação dessa álgebra é definida por . No caso em que X é finito há uma maneira natural de identificar a álgebra de incidência com uma subálgebra da álgebra das matrizes triangulares superiores de ordem \|X\| sobre R (pt) Un conjunto parcialmente ordenado es localmente finito cuando cada intervalo cerrado [a, b] es finito. Para cada poset localmente finito y cada cuerpo de escalares hay un álgebra de incidencia, que es un álgebra asociativa definida como sigue. Los miembros del álgebra de incidencia son las funciones f que asigna a cada intervalo [a, b] un escalar f(a, b). En este conjunto subyacente se definen la adición y la multiplicación por escalar punto a punto, y la "multiplicación" en el álgebra de incidencia es una convolución definida por (es)
dcterms:subject	Algebraic combinatorics Order theory
Wikipage page ID	166980 (xsd:integer)
Wikipage revision ID	1074896799 (xsd:integer)
Link from a Wikipage to another Wikipage	Basis (linear algebra) Derivative Algebraic combinatorics Riemann zeta function Unit (ring theory) Order isomorphism Number line Order theory Convolution Mathematics Matrix (mathematics) Matrix multiplication Normal subgroup Order theory Function (mathematics) Fundamental theorem of arithmetic Generating function Generating functions Gian-Carlo Rota Multiset Möbius function Arithmetic function Combinatorics Commutative ring Empty set Matrix addition Divisor Divisor function Euler product Exponential formula Exponential generating function Finite set Formal power series Number theory Partially ordered set Partition of a set Dirichlet convolution Dirichlet series Graph algebra Simplicial complex Ring (mathematics) Group (mathematics) Isomorphic Hypercube Prime number Difference operator Associative algebra Poset Group ring If and only if Integer Integral Kronecker delta Nathan Jacobson Natural number Category (mathematics) Category algebra Euler characteristic P-group Subalgebra Subset Upper-triangular matrix Divisibility Incidence coalgebra Path algebra Möbius inversion Principle of inclusion-exclusion Locally finite partially ordered set
Link from a Wikipage to an external page	https://archive.org/details/incidencealgebra0000spie
sameAs	Incidence algebra Incidence algebra Incidence algebra Incidence algebra Incidence algebra Incidence algebra Incidence algebra Incidence algebra Incidence algebra Incidence algebra
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