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The contraction of a pair of vertices v_i and v_j of a graph, also called vertex identification, is the operation that produces a graph in which the two nodes v_1 and v_2 are ...

When f:A->B is a ring homomorphism and b is an ideal in B, then f^(-1)(b) is an ideal in A, called the contraction of b and sometimes denoted b^c. The contraction of a prime ...

The contraction of a tensor is obtained by setting unlike indices equal and summing according to the Einstein summation convention. Contraction reduces the tensor rank by 2. ...

In a graph G, contraction of an edge e with endpoints u,v is the replacement of u and v with a single vertex such that edges incident to the new vertex are the edges other ...

Let A be a commutative ring, let C_r be an R-module for r=0, 1, 2, ..., and define a chain complex C__ of the form C__:...|->C_n|->C_(n-1)|->C_(n-2)|->...|->C_2|->C_1|->C_0. ...

An affine transformation in which the scale is reduced.

A tensor t is said to satisfy the double contraction relation when t_(ij)^m^_t_(ij)^n=delta_(mn). (1) This equation is satisfied by t^^^0 = (2z^^z^^-x^^x^^-y^^y^^)/(sqrt(6)) ...

A tensor defined in terms of the tensors which satisfy the double contraction relation.

Tutte's wheel theorem states that every polyhedral graph can be derived from a wheel graph via repeated graph contraction and edge splitting. For example, the figure above ...

A rotation combined with an expansion or geometric contraction.