Generating functions associated to Frobenius algebras

TL;DR

This paper introduces a generating function for graded algebras that quantifies their deviation from finite generation, providing explicit rational functions for certain Frobenius algebra cases.

Contribution

It defines a new generating function for graded algebras and explicitly computes it for some Frobenius endomorphism algebras, linking algebraic properties to rational functions.

Findings

The generating function measures the deviation from finite generation.

Explicit rational functions are derived for specific Frobenius algebras.

The approach connects algebraic structure with generating function analysis.

Abstract

We introduce a generating function associated to the homogeneous generators of a graded algebra that measures how far is this algebra from being finitely generated. For the case of some algebras of Frobenius endomorphisms we describe this generating function explicitly as a rational function.