On the Number of Rumer Diagrams

TL;DR

This paper reviews Rumer diagrams and applies algebraic geometry to count them based on atoms and valence bonds, providing a mathematical foundation for their enumeration.

Contribution

It introduces a novel algebraic geometry approach to enumerate Rumer diagrams with specified atoms and valence bonds, expanding on prior combinatorial methods.

Findings

Established a formula for counting Rumer diagrams

Connected Rumer diagrams to algebraic geometry principles

Enhanced understanding of valence bond configurations

Abstract

In this paper we both review the famous article "Eine fur die Valenztheorie geeignete Basis der binaren Vektorinvarianten" of G. Rumer, E. Teller, and H. Weyl on Rumer diagrams and use a powerful old result from algebraic geometry to enumerate these diagrams with given numbers of atoms and valence bonds.