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Let n objects be picked repeatedly with probability p_i that object i is picked on a given try, with sum_(i)p_i=1. Find the earliest time at which all n objects have been ...

If X is a normed linear space, then the set of continuous linear functionals on X is called the dual (or conjugate) space of X. When equipped with the norm ...

Let p be an odd prime and b a positive integer not divisible by p. Then for each positive odd integer 2k-1<p, let r_k be r_k=(2k-1)b (mod p) with 0<r_k<p, and let t be the ...

The general orthogonal group GO_n(q,F) is the subgroup of all elements of the projective general linear group that fix the particular nonsingular quadratic form F. The ...

Regardless of where one white and one black square are deleted from an ordinary 8×8 chessboard, the reduced board can always be covered exactly with 31 dominoes (of dimension ...

The double-struck capital letter I, I, is a symbol sometimes used instead of Z for the ring of integers. In contrast, the lower case symbol i is used to refer to the ...

Two quantities y and x are said to be inversely proportional (or "in inverse proportion") if y is given by a constant multiple of 1/x, i.e., y=c/x for c a constant. This ...

The middle levels conjecture, also known as revolving door conjecture, posits that the middle layer graph has a Hamilton cycle for every n>=1. The conjecture was proved by ...

For a catastrophically unstable recurrence in one direction, any seed values for consecutive x_j and x_(j+1) will converge to the desired sequence of functions in the ...

A function f(m) is called multiplicative if (m,m^')=1 (i.e., the statement that m and m^' are relatively prime) implies f(mm^')=f(m)f(m^') (Wilf 1994, p. 58). Examples of ...