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Let (A,<=) and (B,<=) be totally ordered sets. Let C=A×B be the Cartesian product and define order as follows. For any a_1,a_2 in A and b_1,b_2 in B, 1. If a_1<a_2, then ...

An oriented graph is a directed graph having no symmetric pair of directed edges. A complete oriented graph is called a tournament. The numbers of oriented graphs on n=1, 2, ...

Three types of n×n matrices can be obtained by writing Pascal's triangle as a lower triangular matrix and truncating appropriately: a symmetric matrix S_n with (S)_(ij)=(i+j; ...

Polysticks, sometimes also known as polyedges, are polyforms obtained from the edges of a regular grid. Square polysticks are polyforms obtained from the edges of a regular ...

Let A be a C^*-algebra. An element a in A is called positive if a=a* and sp(a) subset= R^+, or equivalently if there exists an element b in A such that a=bb^*. For example, ...

The prime distance pd(n) of a nonnegative integer n is the absolute difference between n and the nearest prime. It is therefore true that pd(p)=0 for primes p. The first few ...

The base-4 method of counting in which only the digits 0, 1, 2, and 3 are used. The illustration above shows the numbers 0 to 63 represented in quaternary, and the following ...

A K-rational point is a point (X,Y) on an algebraic curve f(X,Y)=0, where X and Y are in a field K. For example, rational point in the field Q of ordinary rational numbers is ...

Closed forms are known for the sums of reciprocals of even-indexed Lucas numbers P_L^((e)) = sum_(n=1)^(infty)1/(L_(2n)) (1) = sum_(n=1)^(infty)1/(phi^(2n)+phi^(-2n)) (2) = ...

Let R be the class of expressions generated by 1. The rational numbers and the two real numbers pi and ln2, 2. The variable x, 3. The operations of addition, multiplication, ...