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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 ...

An ANOVA in which the number of replicates (sets of identical observations) is restricted to be the same for each factor level (treatment group).

If the total group of the canonical series is divided into two parts, the difference between the number of points in each part and the double of the dimension of the complete ...

Given a point lattice, a cluster is a group of filled cells which are all connected to their neighbors vertically or horizontally.

Let G denote the group of germs of holomorphic diffeomorphisms of (C,0). Then if |lambda|!=1, then G_lambda is a conjugacy class, i.e., all f in G_lambda are linearizable.

Let S(T) be the group of symmetries which map a monohedral tiling T onto itself. The transitivity class of a given tile T is then the collection of all tiles to which T can ...

A zero vector, denoted 0, is a vector of length 0, and thus has all components equal to zero. It is the additive identity of the additive group of vectors.

A Lie algebra is nilpotent when its Lie algebra lower central series g_k vanishes for some k. Any nilpotent Lie algebra is also solvable. The basic example of a nilpotent Lie ...

Let G be a group, then there exists a piecewise linear knot K^(n-2) in S^n for n>=5 with G=pi_1(S^n-K) iff G satisfies 1. G is finitely presentable, 2. The Abelianization of ...

A vertex-transitive graph, also sometimes called a node symmetric graph (Chiang and Chen 1995), is a graph such that every pair of vertices is equivalent under some element ...