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An abstract vector space of dimension n over a field k is the set of all formal expressions a_1v_1+a_2v_2+...+a_nv_n, (1) where {v_1,v_2,...,v_n} is a given set of n objects ...

The sequence a(n) given by the exponents of the highest power of 2 dividing n, i.e., the number of trailing 0s in the binary representation of n. For n=1, 2, ..., the first ...

A giraffe graph is a graph formed by all possible moves of a hypothetical chess piece called a "giraffe" which moves analogously to a knight except that it is restricted to ...

A grammar defining formal language L is a quadruple (N,T,R,S), where N is a finite set of nonterminals, T is a finite set of terminal symbols, R is a finite set of ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

A group G is said to act on a set X when there is a map phi:G×X->X such that the following conditions hold for all elements x in X. 1. phi(e,x)=x where e is the identity ...

A the (first, or internal) Kenmotu point, also called the congruent squares point, is the triangle center constructed by inscribing three equal squares such that each square ...

There are two definitions of a metacyclic group. 1. A metacyclic group is a group G such that both its commutator subgroup G^' and the quotient group G/G^' are cyclic (Rose ...

A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...

A Room square (named after T. G. Room) of order n (for n even) is an arrangement in an (n-1)×(n-1) square matrix of n objects such that each cell is either empty or holds ...