A Combinatorial Theory of Assembly Systems via Generating Functions

TL;DR

This paper introduces a combinatorial framework utilizing generating functions to analyze assembly systems, enabling the study of molecular structures and their equilibrium properties through recursive equations and combinatorial interpretations.

Contribution

It develops a novel combinatorial approach with generating functions for analyzing assembly systems, including recursive characterization and equilibrium analysis.

Findings

Provides recursive equations for assembly characterization

Enables computation of equilibrium probabilities in polymer ensembles

Offers combinatorial interpretations for molecular assembly structures

Abstract

This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid assemblies. The framework accommodates various levels of description, from atoms to complex molecular structures, and provides combinatorial interpretations for each generating function. This approach enables the study of equilibrium behavior and the computation of equilibrium probabilities in polymer ensembles.