Noncommutative algebras, context-free grammars and algebraic Hilbert series. (November 2020)

• Record Type: Journal Article
• Authors: La Scala, Roberto; Piontkovski, Dmitri; Tiwari, Sharwan K.
• Is Part Of: Journal of symbolic computation. Volume 101(2020)
• Page Start: 28
• Page End: 50
• Publication Date: 2020-11
• Subjects: primary 05A15 -- secondary 16E05 68Q42; Algebraic generating functions -- Associative algebras -- Graded homology; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.06.005
• Languages: English
• ISSNs: 0747-7171

Abstract

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.