Hilbert series in the category of trees with contractions

TL;DR

This paper investigates Hilbert series related to modules over categories of trees, demonstrating their algebraic nature and deriving properties of associated generating functions using advanced algebraic techniques.

Contribution

It applies Sam and Snowden's technology to prove algebraicity of Hilbert series in the context of tree categories and explores their implications for generating functions.

Findings

Hilbert series are algebraic in the category of trees with contractions

Generated functions associated with trees have specific algebraic properties

Theoretical framework connects Hilbert series to combinatorial structures

Abstract

We consider Hilbert series associated to modules over various categories of trees. Using the technology of Sam and Snowden, we show that these Hilbert series must be algebraic. We then apply these technical theorems to prove facts about certain natural generating functions associated to trees.