Insertion and Lie Bracket Concerning Finite Sets

TL;DR

This paper explores operations on partitions of finite sets, such as quotient, insertion, composition, and Lie bracket, and discusses their applications in Feynman diagrams and Kontsevich's graphs.

Contribution

It introduces and analyzes operations on partitions of finite sets and applies them to graphical representations in physics and mathematics.

Findings

Defined and examined operations on partitions of finite sets.

Connected these operations to applications in Feynman diagrams.

Linked the operations to Kontsevich's graphs.

Abstract

In this article we discuss the operations of partitions (sequence of disjoint finite subsets) which are quotient, insertion, composition and Lie bracket. Moreover, we discuss applications of those operations for Feymman diagrams and Kontesvich's graphs.