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The number of ways in which a group of n with weights sum_(i=1)^(n)w_i=1 can change a losing coalition (one with sumw_i<1/2) to a winning one, or vice versa. It was proposed ...

Complex infinity is an infinite number in the complex plane whose complex argument is unknown or undefined. Complex infinity may be returned by the Wolfram Language, where it ...

A group having continuous group operations. A continuous group is necessarily infinite, since an infinite group just has to contain an infinite number of elements. But some ...

A degree set is a set of integers that make up a degree sequence. Any set of positive integers is the degree set for some graph, because any odd integer from that set can be ...

A puzzle in which one object is to be converted to another by making a finite number of cuts and reassembling it. The cuts are often, but not always, restricted to straight ...

Down arrow notation is an inverse of the Knuth up-arrow notation defined by evn = lnn (1) evvn = ln^*n (2) evvvn = ln^(**)n, (3) where ln^*n is the number of times the ...

Define the zeta function of a variety over a number field by taking the product over all prime ideals of the zeta functions of this variety reduced modulo the primes. Hasse ...

Let X be a metric space, A be a subset of X, and d a number >=0. The d-dimensional Hausdorff measure of A, H^d(A), is the infimum of positive numbers y such that for every ...

Let Gamma be an algebraic curve in a projective space of dimension n, and let p be the prime ideal defining Gamma, and let chi(p,m) be the number of linearly independent ...

A function of the coordinates which is constant along a trajectory in phase space. The number of degrees of freedom of a dynamical system such as the Duffing differential ...