International Journal of Mathematical Combinatorics Subscription a Subscription Can Be Ordered by a Mail or an Email Directly to Editorial Board Editor-in-chief Editors Combinatorial Field -an Introduction

A combinatorial field WG is a multi-field underlying a graph G, established on a smoothly combinatorial manifold. This paper first presents a quick glance to its mathematical basis with motivation, such as those of why the WORLD is combinatorial? and what is a topological or differentiable combinatorial manifold? After then, we explain how to construct principal fiber bundles on combinatorial manifolds by the voltage assignment technique, and how to establish differential theory, for example, connections on combinatorial manifolds. We also show applications of combinatorial fields to other sciences in this paper.