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The theorem, originally conjectured by Berge (1960, 1961), that a graph is perfect iff neither the graph nor its graph complement contains an odd graph cycle of length at ...

Dyson (1962abc) conjectured that the constant term in the Laurent series product_(1<=i!=j<=n)(1-(x_i)/(x_j))^(a_i) (1) is the multinomial coefficient ...

An arithmetic progression, also known as an arithmetic sequence, is a sequence of n numbers {a_0+kd}_(k=0)^(n-1) such that the differences between successive terms is a ...

A face-centered cubic sphere packing obtained by placing layers of spheres one on top of another. Because there are two distinct ways to place each layer on top of the ...

A number n satisfies the Carmichael condition iff (p-1)|(n/p-1) for all prime divisors p of n. This is equivalent to the condition (p-1)|(n-1) for all prime divisors p of n.

Find consecutive powers, i.e., solutions to x^p-y^q=+/-1, excluding 0 and 1. Catalan's conjecture states that the only solution is 3^2-2^3=1, so 8 and 9 (2^3 and 3^2) are the ...

A cycle double cover of an undirected graph is a collection of cycles that cover each edge of the graph exactly twice. For a polyhedral graph, the faces of a corresponding ...

A double bubble is pair of bubbles which intersect and are separated by a membrane bounded by the intersection. The usual double bubble is illustrated in the left figure ...

A set S is said to be GCD-closed if GCD(x_i,x_j) in S for 1<=i,j<=n.

The generalized Riemann hypothesis conjectures that neither the Riemann zeta function nor any Dirichlet L-series has a zero with real part larger than 1/2. Compare with ...