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Let p(d) be the probability that a random walk on a d-D lattice returns to the origin. In 1921, Pólya proved that p(1)=p(2)=1, (1) but p(d)<1 (2) for d>2. Watson (1939), ...

The number q in a star polygon {p/q}.

A line segment on the boundary of a face, also called a side.

A point at which two polygon edges of a polygon meet.

An equation of the form P(x)=0, where P(x) is a polynomial.

A homogeneous polynomial in two or more variables.

If a polynomial P(x) is divided by (x-r), then the remainder is a constant given by P(r).

The ring R[x] of polynomials in a variable x.

A sequence of polynomials p_i(x), for i=0, 1, 2, ..., where p_i(x) is exactly of degree i for all i.

The difference between the highest and lowest degrees of a polynomial.