The fine- and generative spectra of varieties of monounary algebras

Abstract

In this paper we present recursive formulas to compute the fine spectrum and generative spectrum of each of the varieties of monounary algebras. Hence, an asymptotic or log-asymptotic estimation for the number of n-generated and n-element algebras is given in every variety of monounary algebras. These results provide infinitely many examples of spectra with different orders of magnitude that are asymptotically bigger than any polynomial and smaller than any exponential function.

Locations

• Algebra Universalis - View - PDF