We give a model of the K-ring of the flag varieties in terms of a certain braided Hopf algebra called the Nichols-Woronowicz algebra. Our model is based on the construction of the path operators by C. Lenart and A. Postnikov.

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.