Noncommutative algebras, context-free grammars and algebraic Hilbert series

TL;DR

This paper introduces a class of noncommutative monomial algebras with algebraic Hilbert series, using graded homology and unambiguous context-free grammars, and provides examples of finitely presented graded algebras with this property.

Contribution

It establishes a connection between noncommutative algebra, context-free grammars, and algebraic Hilbert series, expanding understanding of algebraic properties of such algebras.

Findings

Defined a new class of noncommutative monomial algebras with algebraic Hilbert series

Connected algebraic Hilbert series to unambiguous context-free grammars

Provided examples of finitely presented graded algebras with algebraic Hilbert series

Abstract

In this paper we introduce a class of noncommutative (finitely generated) monomial algebras whose Hilbert series are algebraic functions. We use the concept of graded homology and the theory of unambiguous context-free grammars for this purpose. We also provide examples of finitely presented graded algebras whose corresponding leading monomial algebras belong to the proposed class and hence possess algebraic Hilbert series.