Growth functions of finitely generated algebras. (English) Zbl 1314.16014

Fredette, Eric; Kubala, Dan; Nelson, Eric; Wells, Kelsey; Ellingsen, Harold W. jun.

Involve 8, No. 1, 71-74 (2015).

Summary: We study the growth of finitely presented two-generator monomial algebras. In particular, we seek to improve an upper bound found by the last author. Our search lead us to a connection to de Bruijn graphs and a drastically improved bound.

MSC:

16P90	Growth rate, Gelfand-Kirillov dimension
16S15	Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
16S36	Ordinary and skew polynomial rings and semigroup rings
05C38	Paths and cycles
20M25	Semigroup rings, multiplicative semigroups of rings

Keywords:

growth of algebras; growth functions; finitely presented monomial algebras; polynomially bounded growth; exponential growth; finitely generated monomial algebras; de Bruijn graphs

Citations:

Zbl 0840.16019