We prove that the growth functions associated with Artin-monoids of finite type are rational functions whose numerators is equal to 1. We give an explicit formula for the denominator polynomial $N_{M}(t)$ and give three conjectures on it: 1. $N_{M}(t)$ is irreducible up to a factor 1-t, 2. there are $l$-1 real distinct roots of $N_{M}(t)$ on the interval (0,1), and 3. the smallest real root on (0,1) is the unique smallest absolute values of all roots of $N_{M}(t)$.
Publié le : 2008-10-15
Classification:
Artin group,
Artin monoid,
growth function,
zeros of polynomial,
16G10,
16G20,
16G21
@article{1228226750,
author = {Saito, Kyoji},
title = {Growth functions associated with Artin monoids of finite type},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {84},
number = {1},
year = {2008},
pages = { 179-183},
language = {en},
url = {http://dml.mathdoc.fr/item/1228226750}
}
Saito, Kyoji. Growth functions associated with Artin monoids of finite type. Proc. Japan Acad. Ser. A Math. Sci., Tome 84 (2008) no. 1, pp. 179-183. http://gdmltest.u-ga.fr/item/1228226750/