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Let a knot K be parameterized by a vector function v(t) with t in S^1, and let w be a fixed unit vector in R^3. Count the number of local minima of the projection function ...

A plane partition whose solid Ferrers diagram is invariant under the rotation which cyclically permutes the x-, y-, and z-axes. Macdonald's plane partition conjecture gives a ...

Division by zero is the operation of taking the quotient of any number x and 0, i.e., x/0. The uniqueness of division breaks down when dividing by zero, since the product ...

A symbol used to distinguish a third quantity x^('') ("x double prime") from two other related quantities x and x^' ("x prime). Double primes are most commonly used to denote ...

An even permutation is a permutation obtainable from an even number of two-element swaps, i.e., a permutation with permutation symbol equal to +1. For initial set {1,2,3,4}, ...

For any real alpha and beta such that beta>alpha, let p(alpha)!=0 and p(beta)!=0 be real polynomials of degree n, and v(x) denote the number of sign changes in the sequence ...

Gödel's first incompleteness theorem states that all consistent axiomatic formulations of number theory which include Peano arithmetic include undecidable propositions ...

The kth power of a graph G is a graph with the same set of vertices as G and an edge between two vertices iff there is a path of length at most k between them (Skiena 1990, ...

The number of elements in a group G, denoted |G|. If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite ...

Let n be an integer such that n>=lambda_1, where lambda=(lambda_1,lambda_2,...) is a partition of n=|lambda| if lambda_1>=lambda_2>=...>=0, where lambda_i are a sequence of ...