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The W polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. (The corresponding w polynomials are called Lucas polynomials.) They have explicit ...

A free idempotent monoid is a monoid that satisfies the identity x^2=x and is generated by a set of elements. If the generating set of such a monoid is finite, then so is the ...

Let (a)_i and (b)_i be sequences of complex numbers such that b_j!=b_k for j!=k, and let the lower triangular matrices F=(f)_(nk) and G=(g)_(nk) be defined as ...

A monomial is a product of positive integer powers of a fixed set of variables (possibly) together with a coefficient, e.g., x, 3xy^2, or -2x^2y^3z. A monomial can also be ...

The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

Some authors define a general Airy differential equation as y^('')+/-k^2xy=0. (1) This equation can be solved by series solution using the expansions y = ...

Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of ...

The Burnside problem originated with Burnside (1902), who wrote, "A still undecided point in the theory of discontinuous groups is whether the group order of a group may be ...

The second knot polynomial discovered. Unlike the first-discovered Alexander polynomial, the Jones polynomial can sometimes distinguish handedness (as can its more powerful ...