Stirling number and periodic points

TL;DR

This paper introduces the concept of almost realizability as a generalization of realizability for integer sequences and characterizes its intersection with Stirling sequences, advancing understanding of periodic points in dynamical systems.

Contribution

It defines almost realizability and characterizes its intersection with Stirling sequences, providing new insights into the arithmetic properties of periodic points.

Findings

Characterization of the intersection between Stirling sequences and almost realizable sequences.

Introduction of the notion of almost realizability as a generalization of realizability.

Insights into the arithmetic structure of periodic points in dynamical systems.

Abstract

We introduce the notion of almost realizability, an arithmetic generalization of realizability for integer sequences, which is the property of counting periodic points for some map. We characterize the intersection between the set of Stirling sequences (of both the first and the second kind) and the set of almost realizable sequences.