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The sum of sets A and B in a vector space, equal to {a+b:a in A,b in B}.

Polynomials s_k(x) which form the Sheffer sequence for f(t)=-(2t)/(1-t^2) (1) and have exponential generating function ...

A curve y(x) is osculating to f(x) at x_0 if it is tangent at x_0 and has the same curvature there. Osculating curves therefore satisfy y^((k))(x_0)=f^((k))(x_0) for k=0, 1, ...

A singular point such that every neighborhood of the point intersects itself. Pinch points are also called Whitney singularities or branch points.

Polypons are polyforms obtained from dividing a regular triangular grid into 30-30-120 triangles, illustrated above. The numbers of polypons with n=1, 2, ... components are ...

The power polynomials x^n are an associated Sheffer sequence with f(t)=t, (1) giving generating function sum_(k=0)^inftyx^kt^k=1/(1-tx) (2) and exponential generating ...

Let S be a collection of subsets of a set X and let mu:S->[0,infty] be a set function. The function mu is called a premeasure provided that mu is finitely additive, countably ...

For p(z)=a_nz^n+a_(n-1)z^(n-1)+...+a_0, (1) polynomial of degree n>=1, the Schur transform is defined by the (n-1)-degree polynomial Tp(z) = a^__0p(z)-a_np^*(z) (2) = ...

The superdiagonal of a square matrix is the set of elements directly above the elements comprising the diagonal. For example, in the following matrix, the diagonal elements ...

The symbol tau (the lower case Greek letter tau) has many common uses in mathematics, as summarized in the following table. 1. tau(n) is an alternate notation for the divisor ...