Hilbert series of right-angled affine Artin monoid $M(\widetilde{A}^{\infty}_{n})$
Keywords:
Growth rate, Hilbert series, irreducible words.Abstract
It is already proved that the growth rate of all the spherical Artin monoids is less than 4. In this paper, we find the Hilbert series of the associated right-angled affine Artin monoid M and also we discuss the recurrence relations and the growth of the monoid M .
References
Berceanu, B. &Iqbal, Z. (2015). Universal upper bound for
the growth of Artin monoids. Communications in Algebra,
(5):1967- 1982.
Bourbaki, N. (1968). Groupes et algèbres de Lie. Chapitres
-, Elements de Mathematique de Hermann.
Bergman, G. (1978). The diamond lemma for ring theory.
Advances in Mathematics, 29:178 -218.
Cohn, P. M. (2003). Further algebra and applications.
Springer-Verlag, London.
Harpe, P. D. (2000). Topics in geometric group theory. The
University of Chicago Press, America.
Iqbal, Z. (2011). Hilbert series of positive braids. Algebra
Colloquium, special, 1(18):1017- 1028.
Kelley, W. G. & Peterson A. C. (2001). Difference
equations: An introduction with applications. Second
Edition, Academic Press, New York. Pp. 125.