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A bijective map between two metric spaces that preserves distances, i.e., d(f(x),f(y))=d(x,y), where f is the map and d(a,b) is the distance function. Isometries are ...

A ring homomorphism is a map f:R->S between two rings such that 1. Addition is preserved:f(r_1+r_2)=f(r_1)+f(r_2), 2. The zero element is mapped to zero: f(0_R)=0_S, and 3. ...

A number of areas of mathematics have the notion of a "dual" which can be applies to objects of that particular area. Whenever an object A has the property that it is equal ...

A transposition graph G_n is a graph whose nodes correspond to permutations and edges to permutations that differ by exactly one transposition (Skiena 1990, p. 9, Clark ...

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...

The Abel prize is a new mathematics prize of the Norwegian Academy of Science and Letters, dedicated to the memory of Niels Henrik Abel (1802-1829) on the occasion of the ...

A representation of a Lie algebra g is a linear transformation psi:g->M(V), where M(V) is the set of all linear transformations of a vector space V. In particular, if V=R^n, ...

The crystallographic point groups are the point groups in which translational periodicity is required (the so-called crystallography restriction). There are 32 such groups, ...

An arithmetic progression of primes is a set of primes of the form p_1+kd for fixed p_1 and d and consecutive k, i.e., {p_1,p_1+d,p_1+2d,...}. For example, 199, 409, 619, ...

A generalization of the p-adic norm first proposed by Kürschák in 1913. A valuation |·| on a field K is a function from K to the real numbers R such that the following ...