Decomposition Lemmas

TL;DR

This paper introduces two recursive functions derived from interval decomposition into four parts and proves lemmas that reveal their key features, contributing to the theoretical understanding of such functions.

Contribution

It presents new decomposition lemmas for recursive functions based on interval partitioning, advancing theoretical insights in this area.

Findings

Two recursive functions are defined through interval decomposition.

Two lemmas are proved to characterize the features of these functions.

The results enhance understanding of recursive functions derived from interval partitions.

Abstract

We define two recursive functions obtained by decomposition of a given interval into four close parts and prove two lemmas which determine features of these functions.