incidence algebra造句

• The members of the incidence algebra are the ring with unity.
• The Kronecker delta forms the multiplicative identity element of an incidence algebra.
• The delta function in this incidence algebra similarly corresponds to the formal power series 1.
• As a consequence, the M鯾ius function is always a member of the reduced incidence algebra.
• This is a subalgebra of the incidence algebra, and it clearly contains the incidence algebra's identity element and zeta function.
• This is a subalgebra of the incidence algebra, and it clearly contains the incidence algebra's identity element and zeta function.
• Any element of the reduced incidence algebra that is invertible in the larger incidence algebra has its inverse in the reduced incidence algebra.
• Any element of the reduced incidence algebra that is invertible in the larger incidence algebra has its inverse in the reduced incidence algebra.
• Any element of the reduced incidence algebra that is invertible in the larger incidence algebra has its inverse in the reduced incidence algebra.
• Reduced incidence algebras shed light on the theory of generating functions, as alluded to in the case of the natural numbers above.
• On this underlying set one defines addition and scalar multiplication pointwise, and " multiplication " in the incidence algebra is a convolution defined by
• The correspondence between contractions and decompositions of triangles in a multiorder allows one to construct an associative algebra called its " incidence algebra ".
• Incidence algebras of locally finite posets were treated in a number of papers of Gian-Carlo Rota beginning in 1964, and by many later combinatorialists.
• Therefore, ( * * ) is seen as the M鯾ius inversion formula for the incidence algebra of the partially ordered set of all subsets of " A ".
• The Euler characteristic of such a poset is defined as the integer ? ( 0, 1 ), where ? is the M鯾ius function in that poset's incidence algebra.
• Other M鯾ius inversion formulas are obtained when different locally finite partially ordered sets replace the classic case of the natural numbers ordered by divisibility; for an account of those, see incidence algebra.
• Any member of an incidence algebra that assigns the same value to any two intervals that are isomorphic to each other as posets is a member of the "'reduced incidence algebra " '.
• Any member of an incidence algebra that assigns the same value to any two intervals that are isomorphic to each other as posets is a member of the "'reduced incidence algebra " '.
• Any element that is nonzero on all unit arrows has a compositional inverse, and the " M鯾ius function " of a multiorder is defined as the compositional inverse of the zeta function ( constant-one ) in its incidence algebra.