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The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

A group of three elements, also called a triad. A triple is therefore a 3-tuple.

A statement which is rigorously known to be correct. A statement which is not true is called false, although certain statements can be proved to be rigorously undecidable ...

For a set of positive gamma_k, k=0, 1, 2..., Turán's inequalities are given by gamma_k^2-gamma_(k-1)gamma_(k+1)>=0 for k=1, 2, ....

The ultraradical symbol is a notation thet can be used to express solutions not obtainable by finite root extraction. The solution to the irreducible quintic equation x^5+x=a ...

A transformation x^'=Ax is unimodular if the determinant of the matrix A satisfies det(A)=+/-1. A necessary and sufficient condition that a linear transformation transform a ...

Involving one variable, as opposed to two (bivariate) or many (multivariate).

Any discrete finite wavelet transform can be represented as a matrix, and such a wavelet matrix can be computed in O(n) steps, compared to O(nlgn) for the Fourier matrix, ...

A set of three conjectures proposed by Weil in 1942 for extending Riemann hypothesis-like statements to classes of mathematical structures. The conjectures were proved by ...

Let phi(x_1,...,x_m) be an L_(exp) formula, where L_(exp)=L union {e^x} and L is the language of ordered rings L={+,-,·,<,0,1}. Then there exist n>=m and f_1,...,f_s in ...