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If the total group of the canonical series is divided into two parts, the difference between the number of points in each part and the double of the dimension of the complete ...

The chromatic number of a graph is at most the maximum vertex degree Delta, unless the graph is complete or an odd cycle, in which case Delta+1 colors are required.

Vandeghen's (1965) name for the transformation taking points to their isotomic conjugates.

Let A be a commutative ring, let C_r be an R-module for r=0, 1, 2, ..., and define a chain complex C__ of the form C__:...|->C_n|->C_(n-1)|->C_(n-2)|->...|->C_2|->C_1|->C_0. ...

An arrangement of overlapping circles which cover the entire plane. A lower bound for a covering using equivalent circles is 2pi/sqrt(27) (Williams 1979, p. 51).

A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

A functor F is called contravariant if it reverses the directions of arrows, i.e., every arrow f:A-->B is mapped to an arrow F(f):F(B)-->F(A).

A function which arises in the fractional integral of e^(at), given by E_t(nu,a) = (e^(at))/(Gamma(nu))int_0^tx^(nu-1)e^(-ax)dx (1) = (a^(-nu)e^(at)gamma(nu,at))/(Gamma(nu)), ...

For any two integers a and b, suppose d|ab. Then if d is relatively prime to a, then d divides b. This results appeared in Euclid's Elements, Book VII, Proposition 30. This ...