Groups, conics and recurrence relations

Using Recurrence Relations to Count Certain Elements in Symmetric Groups

Let Sn denote the symmetric group of degree n. If 6 ⊆ Sn , then let OMq(6), ODq(6), Œq(6) denote the number of elements in 6 having order: a multiple of q , dividing q, and equal to q , respectively. Similarly, let CMq(6), CDq(6), CEq(6) denote the number of elements in 6 having a cycle (in its disjoint cycle decomposition) of length: a multiple of q , dividing q, and equal to q , respectively....

Recurrence Relations and Generating Functions

Recurrence relations and fast algorithms

We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the values of these linear combinations at certain points, and, vice versa, for evaluating such linear combinations at those points, given the coefficients in t...

( Probabilistic ) Recurrence Relations

The performance attributes of a broad class of randomised algorithms can be described by a recurrence relation of the form T(x) = a(x)+T(H(x)), where a is a function and H(x) is a random variable. For instance, T(x) may describe the running time of such an algorithm on a problem of size x. Then T(x) is a random variable, whose distribution depends on the distribution of H(x). To give high proba...

RECURRENCE RELATIONS , FRACTALS , AND CHAOS 1 Recurrence Relations , Fractals , and Chaos : Implications for Analyzing Gene Structure

The " chaos game " is a well-known algorithm by which one may construct a pictorial representation of an iterative process. The resulting sets are known as fractals and can be mathematically characterized by measures of dimension as well as by their associated recurrence relations. Using the chaos game algorithm, is it possible to derive meaningful structure out of our own genetic encoding, and...