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Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices ...

A Ruth-Aaron pair is a pair of consecutive numbers (n,n+1) such that the sums of the prime factors of n and n+1 are equal. They are so named because they were inspired by the ...

A trinomial coefficient is a coefficient of the trinomial triangle. Following the notation of Andrews (1990), the trinomial coefficient (n; k)_2, with n>=0 and -n<=k<=n, is ...

A universal cellular automaton is a cellular automaton which, like a Turing machine, exhibits universality. von Neumann proved that an automaton consisting of cells with four ...

A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on ...

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 matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...