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One of the Zermelo-Fraenkel axioms which asserts the existence for any set a of a set x such that, for any y of a, if there exists a z satisfying A(y,z), then such z exists ...

One of the Zermelo-Fraenkel axioms which asserts the existence of the empty set emptyset. The axiom may be stated symbolically as exists x forall y(!y in x).

The axiom of Zermelo-Fraenkel set theory which asserts the existence for any set a of the sum (union) x of all sets that are elements of a. The axiom may be stated ...

The recurrence relation (n-1)A_(n+1)=(n^2-1)A_n+(n+1)A_(n-1)+4(-1)^n valid for n=4, 5, ... with A(2)=0 and A(3)=1 and which solves the married couples problem (Dörrie 1965, ...

subjMathematics:Discrete Mathematics:Graph Theory:Cliques The maximal clique polynomial C_G(x) for the graph G may be defined as the polynomial ...

Let (A,<=) and (B,<=) be well ordered sets with ordinal numbers alpha and beta. Then alpha<beta iff A is order isomorphic to an initial segment of B (Dauben 1990, p. 199). ...

A moving average using 15 points having weights -3, -6, -5, 3, 21, 46, 67, 74, 67, 46, 21, 3, -5, -6, and -3. It is sometimes used by actuaries.

The Celmins-Swart snarks are the two snarks on 26 vertices and 39 edges illustrated above. They are implemented in the Wolfram Language as GraphData["CelminsSwartSnark1"] and ...

The dart graph is the 5-vertex graph illustrated above. It is implemented in the Wolfram Language as GraphData["DartGraph"].

The deltoidal icositetrahedral graph is Archimedean dual graph which is the skeleton of the deltoidal icositetrahedron. It is implemented in the Wolfram Language as ...