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Noncommutative algebras, context-free grammars and algebraic Hilbert series

2019; Elsevier BV; Volume: 101; Linguagem: Inglês

10.1016/j.jsc.2019.06.005

1095-855X

Roberto La Scala, Dmitri Piontkovski, Sharwan K. Tiwari,

semigroups and automata theory

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.