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 = 2â€¦ (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.

In this note we continue the study of gaps in samples of geometric random variables originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables.â€¦ (More)

A composition of an integer n is called Carlitz if adjacent parts are different. Several characteristics of random Carlitz compositions have been studied recently by Knopfmacher and Prodinger. Weâ€¦ (More)

For T E GL,(F,), let Q , ( T ) be the number of irreducible factors that the characteristic polynomial of T has. We prove that, for any fixed x , # { T : R,(T)<log n + x ) / # G L , , ( F , ) + ( l /â€¦ (More)

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,â€¦ (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, andâ€¦ (More)

For a subsetS of positive integers let (n,S)be the set of partitions ofn into summands that are elements of S. For every Î» âˆˆ (n,S), let Mn(Î») be the number of parts, with multiplicity, that Î» has.â€¦ (More)