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The double-struck capital letter I, I, is a symbol sometimes used instead of Z for the ring of integers. In contrast, the lower case symbol i is used to refer to the ...

A block graph, also called a clique tree, is a simple graph in which every block is a complete graph. The numbers of connected block graphs on n=1, 2, ... vertices are 1, 1, ...

"The" Jacobi identity is a relationship [A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0,, (1) between three elements A, B, and C, where [A,B] is the commutator. The elements of a Lie algebra ...

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

One of the operations of addition, subtraction, multiplication, division, and integer (or rational) root extraction.

Suppose a,b in N, n=ab+1, and x_1, ..., x_n is a sequence of n real numbers. Then this sequence contains a monotonic increasing (decreasing) subsequence of a+1 terms or a ...

A set which contains a nonnegative integral number of elements is said to be finite. A set which is not finite is said to be infinite. A finite or countably infinite set is ...

Model completion is a term employed when existential closure is successful. The formation of the complex numbers, and the move from affine to projective geometry, are ...

Let G be a group and theta n permutation of G. Then theta is an orthomorphism of G if the self-mapping nu of G defined by nu(x)=x^(-1)theta(x) is also an permutation of G.

A reduced root system is a root system R satisfying the additional property that, if alpha in R, then the only multiples of alpha in R are +/-alpha.