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Numbers 1, alpha_1, ..., alpha_L are rationally independent iff under the action of rotation rho_(alpha_1)×...×rho_(alpha_L) on the L-dimensional torus, every orbit is ...

In computer science, a pop is an action which removes the initial element from the top of a queue or stack, turning the list (a_1, a_2, ..., a_n) into (a_2, ..., a_n) and ...

Given a group action G×F->F and a principal bundle pi:A->M, the associated fiber bundle on M is pi^~:A×F/G->M. (1) In particular, it is the quotient space A×F/G where ...

A continuous homomorphism of a group into the nonzero complex numbers. A multiplicative character omega gives a group representation on the one-dimensional space C of complex ...

Transitivity is a result of the symmetry in the group. A group G is called transitive if its group action (understood to be a subgroup of a permutation group on a set Omega) ...

A group set is a set whose elements are acted on by a group. If the group G acts on the set S, then S is called a G-set. Let G be a group and let S be a G-set. Then for every ...

A plane tiling is said to be isohedral if the symmetry group of the tiling acts transitively on the tiles, and n-isohedral if the tiles fall into n orbits under the action of ...

A two-person game where each of the players can take as long as he likes to prepare his move, but the other can take advantage of his hesitation. In this conflict situation, ...

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, ...

A means of describing how one state develops into another state over the course of time. Technically, a dynamical system is a smooth action of the reals or the integers on ...