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The Krohn-Rhodes complexity, also called the group complexity or simply "the complexity," of a finite semigroup S is the smallest number of groups in a wreath product of ...

A polynomial is called logarithmically concave (or log-concave) if the sequence of its coefficients is logarithmically concave. If P(x) is log-convex and Q(x) is unimodal, ...

The power A^n of a matrix A for n a nonnegative integer is defined as the matrix product of n copies of A, A^n=A...A_()_(n). A matrix to the zeroth power is defined to be the ...

A group G is nilpotent if the upper central sequence 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... of the group terminates with Z_n=G for some n. Nilpotent groups have the property that ...

An irreducible algebraic integer which has the property that, if it divides the product of two algebraic integers, then it divides at least one of the factors. 1 and -1 are ...

A relation is any subset of a Cartesian product. For instance, a subset of A×B, called a "binary relation from A to B," is a collection of ordered pairs (a,b) with first ...

Suppose for every point x in a manifold M, an inner product <·,·>_x is defined on a tangent space T_xM of M at x. Then the collection of all these inner products is called ...

A simple pole of an analytic function f is a pole of order one. That is, (z-z_0)f(z) is an analytic function at the pole z=z_0. Alternatively, its principal part is c/(z-z_0) ...

If the top and bottom bases of a solid are equal in area, lie in parallel planes, and every section of the solid parallel to the bases is equal in area to that of the base, ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...