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Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. The term "discrete mathematics" is therefore used in ...

An extended rooted binary tree satisfying the following conditions: 1. Every node has two children, each colored either red or black. 2. Every tree leaf node is colored ...

The spherical harmonics can be generalized to vector spherical harmonics by looking for a scalar function psi and a constant vector c such that M = del x(cpsi) (1) = psi(del ...

Discrete Mathematics

A generalization of Fermat's last theorem which states that if a^x+b^y=c^z, where a, b, c, x, y, and z are any positive integers with x,y,z>2, then a, b, and c have a common ...

Given a factor a of a number n=ab, the cofactor of a is b=n/a. A different type of cofactor, sometimes called a cofactor matrix, is a signed version of a minor M_(ij) defined ...

The extension of a, an ideal in commutative ring A, in a ring B, is the ideal generated by its image f(a) under a ring homomorphism f. Explicitly, it is any finite sum of the ...

Linnik's constant L is the constant appearing in Linnik's theorem. Heath-Brown (1992) has shown that L<=5.5, and Schinzel, Sierpiński, and Kanold (Ribenboim 1989) have ...

Mann's theorem is a theorem widely circulated as the "alpha-beta conjecture" that was subsequently proven by Mann (1942). It states that if A and B are sets of integers each ...

A short set of data that proves the primality of a number. A certificate can, in general, be checked much more quickly than the time required to generate the certificate. ...