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There are certain optimization problems that become unmanageable using combinatorial methods as the number of objects becomes large. A typical example is the traveling ...

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 ...

A maximal clique is a clique that cannot be extended by including one more adjacent vertex, meaning it is not a subset of a larger clique. A maximum clique (i.e., clique of ...

A computation is an operation that begins with some initial conditions and gives an output which follows from a definite set of rules. The most common example are ...

A Gröbner basis G for a system of polynomials A is an equivalence system that possesses useful properties, for example, that another polynomial f is a combination of those in ...

A maximum spanning tree is a spanning tree of a weighted graph having maximum weight. It can be computed by negating the weights for each edge and applying Kruskal's ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

For any constructible function f, there exists a function P_f such that for all functions t, the following two statements are equivalent: 1. There exists an algorithm A such ...

Informally, a function f:{0,1}^(l(n))×{0,1}^n->{0,1}^(m(n)) is a trapdoor one-way function if 1. It is a one-way function, and 2. For fixed public key y in {0,1}^(l(n)), ...

The sequence produced by sorting the digits of a number and adding them to the previous number. The values starting with n=1, 2, ... are 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, ...