# On the growth of algebras, semigroups, and hereditary languages

## TL;DR

This paper characterizes the possible asymptotic growth functions of semigroups, hereditary languages, and algebras, providing a comprehensive understanding of their growth behaviors.

## Contribution

It identifies the set of all functions that can serve as growth functions for these algebraic structures, up to asymptotic equivalence.

## Key findings

- Characterization of growth functions for semigroups
- Characterization of growth functions for hereditary languages
- Characterization of growth functions for algebras

## Abstract

We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras.