Acyclic Jacobi Diagrams

TL;DR

This paper introduces a new combinatorial model for acyclic Jacobi diagrams, representing them as algebras of words, which facilitates combinatorial analysis and offers new insights into their structure.

Contribution

The paper presents a novel word-based combinatorial framework for acyclic Jacobi diagrams, enabling new approaches to their study and understanding.

Findings

Provides a new algebraic model for acyclic Jacobi diagrams

Offers a combinatorial approach to analyze diagram spaces

Yields fresh insights into known properties of these diagrams

Abstract

We propose a simple new combinatorial model to study spaces of acyclic Jacobi diagrams, in which they are identified with algebras of words modulo operations. This provides a starting point for a word-problem type combinatorial investigation of such spaces, and provides fresh insights on known results.