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A lottery in which three numbers are picked at random from the integers 1-14.

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

The quadratic class number constant is a constant related to the average behavior of class numbers of real quadratic fields. It is given by Q = product_(p)[1-1/(p^2(p+1))] ...

A superior highly composite number is a positive integer n for which there is an e>0 such that (d(n))/(n^e)>=(d(k))/(k^e) for all k>1, where the function d(n) counts the ...

For a given m, determine a complete list of fundamental binary quadratic form discriminants -d such that the class number is given by h(-d)=m. Heegner (1952) gave a solution ...

The measurable space (S^',S^') into which a random variable from a probability space is a measurable function.

The minimal polynomial of an algebraic number zeta is the unique irreducible monic polynomial of smallest degree p(x) with rational coefficients such that p(zeta)=0 and whose ...

The associated Stirling numbers of the first kind d_2(n,k)=d(n,k) are defined as the number of permutations of a given number n having exactly k permutation cycles, all of ...

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

What is the probability that a chord drawn at random on a circle of radius r (i.e., circle line picking) has length >=r (or sometimes greater than or equal to the side length ...