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Find the minimum number f(n) of subsets in a separating family for a set of n elements, where a separating family is a set of subsets in which each pair of adjacent elements ...

The operator tpartial/partialr that can be used to derive multivariate formulas for moments and cumulants from corresponding univariate formulas. For example, to derive the ...

The Kirchhoff index Kf, also simply called the resistance and denoted R (Lukovits et al. 1999), of a connected graph G on n nodes is defined by ...

The kiss surface is the quintic surface of revolution given by the equation x^2+y^2=(1-z)z^4 (1) that is closely related to the ding-dong surface. It is so named because the ...

Knuth's up-arrow notation is a notation invented by Knuth (1976) to represent large numbers in which evaluation proceeds from the right (Conway and Guy 1996, p. 60): m^n ...

For every ring containing p spheres, there exists a ring of q spheres, each touching each of the p spheres, where 1/p+1/q=1/2, (1) which can also be written (p-2)(q-2)=4. (2) ...

Let alpha(x) be a step function with the jump j(x)=(N; x)p^xq^(N-x) (1) at x=0, 1, ..., N, where p>0,q>0, and p+q=1. Then the Krawtchouk polynomial is defined by ...

The simplest interpretation of the Kronecker delta is as the discrete version of the delta function defined by delta_(ij)={0 for i!=j; 1 for i=j. (1) The Kronecker delta is ...

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...

A procedure for decomposing an N×N matrix A into a product of a lower triangular matrix L and an upper triangular matrix U, LU=A. (1) LU decomposition is implemented in the ...