Recurrence relations versus succession rules

TL;DR

This paper introduces a method to convert constant-coefficient recurrence relations into finite succession rules, aiding in combinatorial enumeration and positivity testing of sequences.

Contribution

The paper presents a novel approach to derive finite succession rules from C-recurrences, linking recurrence relations with combinatorial enumeration tools.

Findings

Method successfully converts C-recurrences to succession rules

Application as a positivity test for sequences

Enhances combinatorial enumeration techniques

Abstract

In this paper we present a method to pass from a recurrence relation having constant coefficients (in short, a C-recurrence) to a finite succession rule defining the same number sequence. We recall that succession rules are a recently studied tool for the enumeration of combinatorial objects related to the ECO method. We also discuss the applicability of our method as a test for the positivity of a number sequence.