Mathematica Eterna
Open Access

Abstract

Iterating Linear Causal Recurrence Relations

Mircea Ion Cˆırnu

The iteration formula of the linear causal recurrence relations with variable coefficients in a ring is given. Using this formula, the initial value problem for such relations is solved. Particular cases and applications to combinatorics, especially to sequences of numbers and polynomials, and to quicksort theory are given. The paper continues the author’s concerns related to the study of linear and non-linear recurrence relations, published in a series of articles cited in References.