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The fraction of odd values of the partition function P(n) is roughly 50%, independent of n, whereas odd values of Q(n) occur with ever decreasing frequency as n becomes ...

A problem posed by L. Collatz in 1937, also called the 3x+1 mapping, 3n+1 problem, Hasse's algorithm, Kakutani's problem, Syracuse algorithm, Syracuse problem, Thwaites ...

Let P(G) denote the chromatic polynomial of a finite simple graph G. Then G is said to be chromatically unique if P(G)=P(H) implies that G and H are isomorphic graphs, in ...

Cubic nonhamiltonian graphs are nonhamiltonian graphs that are also cubic. The numbers of connected cubic nonhamiltonian graphs on n=10, 12, ... nodes are 2, 5, 35, 219, ...

In celestial mechanics, the fixed path a planet traces as it moves around the sun is called an orbit. When a group G acts on a set X (this process is called a group action), ...

A 2-variable oriented knot polynomial P_L(a,z) motivated by the Jones polynomial (Freyd et al. 1985). Its name is an acronym for the last names of its co-discoverers: Hoste, ...

A second-order linear Hermitian operator is an operator L^~ that satisfies int_a^bv^_L^~udx=int_a^buL^~v^_dx. (1) where z^_ denotes a complex conjugate. As shown in ...

The Laplacian for a scalar function phi is a scalar differential operator defined by (1) where the h_i are the scale factors of the coordinate system (Weinberg 1972, p. 109; ...

Martin Gardner (1975) played an April Fool's joke by asserting that the map of 110 regions illustrated above (left figure) required five colors and constitutes a ...

The terms "measure," "measurable," etc. have very precise technical definitions (usually involving sigma-algebras) that can make them appear difficult to understand. However, ...