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A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. The most common type of vertex ...

The constants lambda_(m,n)=inf_(r in R_(m,n))sup_(x>=0)|e^(-x)-r(x)|, where r(x)=(p(x))/(q(x)), p and q are mth and nth order polynomials, and R_(m,n) is the set of all ...

The absolute square of a complex number z, also known as the squared norm, is defined as |z|^2=zz^_, (1) where z^_ denotes the complex conjugate of z and |z| is the complex ...

An encoding is a way of representing a number or expression in terms of another (usually simpler) one. However, multiple expressions can also be encoded as a single ...

Little's law states that, under steady state conditions, the average number of items in a queuing system equals the average rate at which the items arrive multiplied by the ...

A generalization of simple majority voting in which a list of quotas {q_0,...,q_n} specifies, according to the number of votes, how many votes an alternative needs to win ...

The number of ways N(m,n) of finding a subrectangle with an m×n rectangle can be computed by counting the number of ways in which the upper right-hand corner can be selected ...

A formula for the permanent of a matrix perm(a_(ij))=(-1)^nsum_(s subset= {1,...,n})(-1)^(|s|)product_(i=1)^nsum_(j in s)a_(ij), where the sum is over all subsets of ...

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

A Mersenne prime is a Mersenne number, i.e., a number of the form M_n=2^n-1, that is prime. In order for M_n to be prime, n must itself be prime. This is true since for ...