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Macdonald's constant term conjectures are related to root systems of Lie algebras (Macdonald 1982, Andrews 1986). They can be regarded as generalizations of Dyson's ...

Let f(z) be an entire function such that f(n) is an integer for each positive integer n. Then Pólya (1915) showed that if lim sup_(r->infty)(lnM_r)/r<ln2=0.693... (1) (OEIS ...

An algorithm which can be used to find integer relations between real numbers x_1, ..., x_n such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. Although the algorithm ...

A factor of a polynomial P(x) of degree n is a polynomial Q(x) of degree less than n which can be multiplied by another polynomial R(x) of degree less than n to yield P(x), ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

Let B_t={B_t(omega)/omega in Omega}, t>=0, be one-dimensional Brownian motion. Integration with respect to B_t was defined by Itô (1951). A basic result of the theory is that ...

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

Rule 110 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

Smale's problems are a list of 18 challenging problems for the twenty-first century proposed by Field medalist Steven Smale. These problems were inspired in part by Hilbert's ...

Picking two independent sets of points x and y from a unit uniform distribution and placing them at coordinates (x,y) gives points uniformly distributed over the unit square. ...