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Chevalley's theorem, also known as the Chevalley-Waring theorem, states that if f is a polynomial in F[x_1,...,x_n], where F is a finite field of field characteristic p, and ...

A notation for large numbers due to Steinhaus (1999). In circle notation, is defined as n in n squares, where numbers written inside squares (and triangles) are interpreted ...

Take K a number field and m a divisor of K. A congruence subgroup H is defined as a subgroup of the group of all fractional ideals relative prime to m (I_K^m) that contains ...

All closed surfaces, despite their seemingly diverse forms, are topologically equivalent to spheres with some number of handles or cross-caps. The traditional proof follows ...

Coding theory, sometimes called algebraic coding theory, deals with the design of error-correcting codes for the reliable transmission of information across noisy channels. ...

A coloring of plane regions, link segments, etc., is an assignment of a distinct labeling (which could be a number, letter, color, etc.) to each component. Coloring problems ...

Combinatorial geometry is a blending of principles from the areas of combinatorics and geometry. It deals with combinations and arrangements of geometric objects and with ...

The expected number of trials needed to collect a complete set of n different objects when picked at random with repetition is nH_n (Havil 2003, p. 131). For n=1, 2, ..., the ...

A completely positive matrix is a real n×n square matrix A=(a_(ij)) that can be factorized as A=BB^(T), where B^(T) stands for the transpose of B and B is any (not ...

There are at least two meanings on the word congruent in mathematics. Two geometric figures are said to be congruent if one can be transformed into the other by an isometry ...