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A hexagon (not necessarily regular) on whose polygon vertices a circle may be circumscribed. Let sigma_i=Pi_i(a_1^2,a_2^2,a_3^2,a_4^2,a_5^2,a_6^2) (1) denote the ith-order ...

A cyclic polygon is a polygon with vertices upon which a circle can be circumscribed. Since every triangle has a circumcircle, every triangle is cyclic. It is conjectured ...

Given binomial coefficient (N; k), write N-k+i=a_ib_i, for 1<=i<=k, where b_i contains only those prime factors >k. Then the number of i for which b_i=1 (i.e., for which all ...

The study of designs and, in particular, necessary and sufficient conditions for the existence of a block design.

A square matrix A is called diagonally dominant if |A_(ii)|>=sum_(j!=i)|A_(ij)| for all i. A is called strictly diagonally dominant if |A_(ii)|>sum_(j!=i)|A_(ij)| for all i. ...

A polynomial Z_G(q,v) in two variables for abstract graphs. A graph with one graph vertex has Z=q. Adding a graph vertex not attached by any graph edges multiplies the Z by ...

sum_(1<=k<=n)(n; k)((-1)^(k-1))/(k^m)=sum_(1<=i_1<=i_2<=...<=i_m<=n)1/(i_1i_2...i_m), (1) where (n; k) is a binomial coefficient (Dilcher 1995, Flajolet and Sedgewick 1995, ...

A series suma(n)e^(-lambda(n)z), where a(n) and z are complex and {lambda(n)} is a monotonic increasing sequence of real numbers. The numbers lambda(n) are called the ...

The disjoint union of two sets A and B is a binary operator that combines all distinct elements of a pair of given sets, while retaining the original set membership as a ...

An n-dimensional disk (sometimes spelled "disc") of radius r is the collection of points of distance <=r (closed disk) or <r (open disk) from a fixed point in Euclidean ...