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The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method ...

A sum-free set S is a set for which the intersection of S and the sumset S+S is empty. For example, the sum-free sets of {1,2,3} are emptyset, {1}, {2}, {3}, {1,3}, and ...

A generating function f(x) is a formal power series f(x)=sum_(n=0)^inftya_nx^n (1) whose coefficients give the sequence {a_0,a_1,...}. The Wolfram Language command ...

There are two problems commonly known as the subset sum problem. The first ("given sum problem") is the problem of finding what subset of a list of integers has a given sum, ...

Given a pick-7 lottery with 23 numbers that pays a prize to anyone matching at least 4 of the 7 numbers, there is a set of 253 tickets that guarantees a win. This set ...

An independent vertex set of a graph G is a subset of the vertices such that no two vertices in the subset represent an edge of G. The figure above shows independent sets ...

The Lambert W-function, also called the omega function, is the inverse function of f(W)=We^W. (1) The plot above shows the function along the real axis. The principal value ...

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...