Combinatorial Structure in Nevanlinna Theory

Abstract

In "Meromorphic Functions and Analytic Curves", H. and F. J. Weyl identified an intriguing connection between holomorphic curves and their associated curves, which they referred to as the "peculiar relation". In this paper, we present a generalization of the Weyl peculiar relation and investigate a combinatorial structure underlying the Weyl--Ahlfors theory via standard Young tableaux. We also provide an alternative proof of the Second Main Theorem from the viewpoint of comparing the order functions $iT_p$ and $T_i\{\mathbf{X}^{(p)}\}$.