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A number of attractive 8-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

A totally imaginary field is a field with no real embeddings. A general number field K of degree n has s real embeddings (0<=s<=n) and 2t imaginary embeddings (0<=t<=n/2), ...

A set of n cells in an n×n square such that no two come from the same row and no two come from the same column. The number of transversals of an n×n square is n! (n ...

In statistics, a trial is a single performance of well-defined experiment (Papoulis 1984, p. 25), such as the flipping of a coin, the generation of a random number, the ...

The vertex count of a graph g, commonly denoted V(g) or |g|, is the number of vertices in g. In other words, it is the cardinality of the vertex set. The vertex count of a ...

If each of two curves meets the line at infinity in distinct, nonsingular points, and if all their intersections are finite, then if to each common point there is attached a ...

The letter O is used for a number of different purposes in mathematics. The double-struck O is sometimes used to represent octonions. The symbols O(x) (sometimes called the ...

If a sequence takes only a small number of different values, then by regarding the values as the elements of a finite field, the Berlekamp-Massey algorithm is an efficient ...

The number of bases in which 1/p is a repeating decimal (actually, repeating b-ary) of length l is the same as the number of fractions 0/(p-1), 1/(p-1), ..., (p-2)/(p-1) ...

If p is a prime >3, then the numerator of the harmonic number H_(p-1)=1+1/2+1/3+...+1/(p-1) (1) is divisible by p^2 and the numerator of the generalized harmonic number ...