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Symmetry operations include the improper rotation, inversion operation, mirror plane, and rotation. Together, these operations create 32 crystal classes corresponding to the ...

A Taylor graph is a distance-regular graph with intersection array {k,mu,1;1,mu,k}. A Taylor graph with these parameters has 2(k+1) vertices. The crown graphs K_2 square ...

Given two additive groups (or rings, or modules, or vector spaces) A and B, the map f:A-->B such that f(a)=0 for all a in A is called the zero map. It is a homomorphism in ...

An International Standard Book Number (ISBN) is a code used to uniquely identify a book together. It also uniquely encodes the book's publisher and includes information about ...

A multiplication table is an array showing the result of applying a binary operator to elements of a given set S. For example, the following table is the multiplication table ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

The Lucas numbers are the sequence of integers {L_n}_(n=1)^infty defined by the linear recurrence equation L_n=L_(n-1)+L_(n-2) (1) with L_1=1 and L_2=3. The nth Lucas number ...

Multiply all the digits of a number n by each other, repeating with the product until a single digit is obtained. The number of steps required is known as the multiplicative ...

The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

The space groups in two dimensions are called wallpaper groups. In three dimensions, the space groups are the symmetry groups possible in a crystal lattice with the ...