If a recursive tree is selected uniformly at random from among all recursive trees on n vertices, then the distribution of the maximum in-degree is given asymptotically by the following theorem: for… (More)

Choose a random polynomial f uniformly from among the qd(q − 1) polynomials of degree d in Fq[x]. Let ck be the number of cycles of length k in the directed graph on Fq with edges {(v, f(v))}v∈Fq .… (More)

Let fin be the expected order of a random permutation, that is, the arithmetic mean of the orders of the elements in the symmetric group Sn. We prove that log/in ~ c\/(n/\ogn) as n -> oo, where c = 2… (More)

Meir and Moon studied the distribution of the maximum degree for simply generated families of trees. We have sharper results for the special case of labelled trees.

Let GLn(FQ) denote the set of invertible nxn matrices with entries in the finite field Fq. Pick a random Te GLn(FQ), and factor its characteristic polynomial. How will it factor? Theorem 1.1 is,… (More)

If S is a cofinite set of positive integers, an “S-restricted composition of n” is a sequence of elements of S, denoted ~λ = (λ1, λ2, . . . ), whose sum is n. For uniform random S-restricted… (More)

A par t i t ion of n is a mul t i se t of positive integers whose sum is n. The summands , i.e., the e lements of the mult iset , are called parts. Let 9 , be the set of all par t i t ions of n, and… (More)

The unit sphere, centered at the origin in R, has a dense set of points with rational coordinates. We give an elementary proof of this fact that includes explicit bounds on the complexity of the… (More)