THE GROWTH OF FREE INVERSE MONOIDS
Abstract
Abstract We compute the rate of exponential growth of the free inverse monoid of rank r (and hence an upper bound on the corresponding rate for all r -generated inverse monoids and semigroups). This turns out to be an algebraic number strictly between the obvious bounds of 2 r − 1 $2r-1$ 2 r minus 1 and 2 r $2r$ 2 r , tending to 2 r $2r$ 2 r as the rank tends to infinity. We also find an explicit expression for the exponential growth rate of the number of idempotents, and prove that this tends to e ( 2 r − 1 ) $\sqrt {e(2r-1)}$ StartRoot e left parenthesis 2 r minus 1 right parenthesis EndRoot as r → ∞ $r \to \infty $ r right arrow infinity .
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Differential Equations and Dynamical Systems
Advanced Topology and Set Theory
Publication details
- Journal / source
- Journal of the Institute of Mathematics of Jussieu
- Publisher
- Cambridge University Press (CUP)
- Volume
- 25
- Issue
- 4
- Pages
- 2047–2067
- Publication date
- 11 June 2026
- Language
- EN