On additive functionals admitting exceptional sets

Additive functionals on multiway search trees

We derive asymptotics of moments and limiting distributions, under the random permutation model on m-ary search trees on n keys, of functionals that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal path length, and the socalled shape functional fall under this framework. The limiting behavior of these functionals exhibi...

BLT-sets admitting the symmetric group S4

We describe a set of subgroups isomorphic to S4 in PΓO(5, q), q ≡ 5(6), and prove that they belong to exactly two different conjugacy classes. As an application we use a representative group in each of the conjugacy classes to construct a number of BLT-sets of Q(4, q), some of which were previously found by computer in [5] (see also [4]), others of which are new.

Exceptional Sets and Fiber Products

Exceptional sets where fibers have dimensions higher than the generic fiber dimension are of interest in mathematics and in application areas, such as the theory of overconstrained mechanisms. We show that fiber products promote such sets to become irreducible components, whereupon they can be found using techniques from numerical algebraic geometry for computing the irreducible decomposition. ...

Limiting distributions for additive functionals on Catalan trees

Additive tree functionals represent the cost of many divide-andconquer algorithms. We derive the limiting distribution of the additive functionals induced by toll functions of the form (a) nα when α > 0 and (b) log n (the so-called shape functional) on uniformly distributed binary search trees, sometimes called Catalan trees. The Gaussian law obtained in the latter case complements the central ...

Additive functionals on spaces with non-absolutely-continuous norm