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The stability index Z^_(G) of a graph G is defined by Z^_=sum_(k=0)^(|_n/2_|)|c_(2k)|, where c_k is the kth coefficient of the characteristic polynomial and |_n_| denotes the ...

Start with an integer n, known as the digitaddition generator. Add the sum of the digitaddition generator's digits to obtain the digitaddition n^'. A number can have more ...

A repunit prime is a repunit (i.e., a number consisting of copies of the single digit 1) that is also a prime number. The base-10 repunit (possibly probable) primes ...

The nesting of two or more functions to form a single new function is known as composition. The composition of two functions f and g is denoted f degreesg, where f is a ...

A sequence of random variates X_0, X_1, ... is called absolutely fair if for n=1, 2, ..., <X_1>=0 and <X_(n+1)|X_1,...,X_n>=0 (Feller 1971, p. 210).

The arc set of a directed graph is the set of all arcs (directed edges) of the graph. The arc set for a directed graph g is given in the Wolfram Language by EdgeList[g].

For an algebra A, the associator is the trilinear map A×A×A->A given by (x,y,z)=(xy)z-x(yz). The associator is identically zero iff A is associative.

A set is said to be bounded from below if it has a lower bound. Consider the real numbers with their usual order. Then for any set M subset= R, the infimum infM exists (in R) ...

The series producing Brun's constant converges even if there are an infinite number of twin primes, first proved by Brun (1919).

There are two completely different definitions of Cayley numbers. The first and most commonly encountered type of Cayley number is the eight elements in a Cayley algebra, ...