On right-angled spherical Artin monoid of type Dn

Abstract

Recently Berceanu and Iqbal proved that the growth rate of all the spherical Artin monoids is bounded above by 4. In this paper we compute the Hilbert series of the right-angled spherical Artin monoid M(Dn∞)$\begin{array}{} M({D}^{\infty}_{n}) \end{array} $ and graphically prove that growth rate is bounded by 4. We also discuss its recurrence relations and other main properties.

Keywords

• canonical words
• hilbert series
• growth rate
• 02.10.ox
• 02.40.re
• 02.20.bb
• 02.30.lt