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If the abstract simplicial complex S is isomorphic with the vertex scheme of the simplicial complex K, then K is said to be a geometric realization of S, and is uniquely ...

The Heisenberg group H^n in n complex variables is the group of all (z,t) with z in C^n and t in R having multiplication (w,t)(z,t^')=(w+z,t+t^'+I[w^*z]) (1) where w^* is the ...

The correspondence which relates the Hanoi graph to the isomorphic graph of the odd binomial coefficients in Pascal's triangle, where the adjacencies are determined by ...

A Meeussen sequence is an increasing sequence of positive integers (m_1, m_2, ...) such that m_1=1, every nonnegative integer is the sum of a subset of the {m_i}, and each ...

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). ...

An important result in ergodic theory. It states that any two "Bernoulli schemes" with the same measure-theoretic entropy are measure-theoretically isomorphic.

Every Lie algebra L is isomorphic to a subalgebra of some Lie algebra A^-, where the associative algebra A may be taken to be the linear operators over a vector space V.

The point group C_1 is a group on a single element that is isomorphic to the trivial group. Its character table is given below. C_1 1 1 1

A graph G is called d-polytopal if there exists a d-dimensional convex polytope P such that the vertices and edges of G are in a one-to-one incidence-preserving ...

The prime subfield of a field F is the subfield of F generated by the multiplicative identity 1_F of F. It is isomorphic to either Q (if the field characteristic is 0), or ...