In this work we provide low rank estimations for coordinate sequences of linear recurrent sequences (LRS) of maximal period (MP) over Galois ring R = GR(pn, r), p ≥ 5, r ≥ 2, with numbers s such that s = kr + 2, k ∈ N0.

We derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius R and taking the limit as R → ∞. These relations take the form of mass integrals, associated with extraneous momenta (relative to the lower dimension), and produce the result in the higher dimension.

We define the excedance number on the complex reflection groups and compute its multidistribution with the number of fixed points on the set of involutions in these groups. We use some recurrences and generating functions manipulations to obtain our results.

Using the Poincaré–Perron theorem on the asymptotics of the solutions of linear recurrences it is proved that for a class of q-continued fractions the value of the continued fraction is given by a quotient of the solution and its q-shifted value of the corresponding qfunctional equation. r 2003 Elsevier Inc. All rights reserved.

The paper is devoted to the methods of solving simultaneous recurrences. Specifically, we discuss transformation of matrix recurrences to regular recurrences and propose a way of solving special matrix recurrences of order three by their decomposition to matrix recurrences of order two.

The paper investigates relationships between algebraic expressions and graphs. Using the decomposition method we generate special simultaneous systems of linear recurrences for sizes of graph expressions. We propose techniques which provide closed-form solutions for these systems.

By using a generating function approach it is shown that certain functionals of digitial expansion (related to speciic nite linear recurrences), e.g. the number of speciic digital patterns, satisfy a central limit theorem. We provide asymptotic expansions for mean value and variance and prove a global and a local limit law.