منابع مشابه
On Singular Artin Monoids
In this paper we study some combinatorial aspects of the singular Artin monoids. Firstly, we show that a singular Artin monoid SA can be presented as a semidirect product of a graph monoid with its associated Artin group A. Such a decomposition implies that a singular Artin monoid embeds in a group. Secondly, we give a solution to the word problem for the FC type singular Artin monoids. Afterwa...
متن کاملSingular Artin Monoids of Finite Coxeter Type Are Automatic
We consider the positive singular and the singular Artin monoids of finite type. These have been the subject of a great deal of recent research and the main purpose of this paper is to prove that these monoids are automatic. In order to do this we establish a new criterion for proving monoids automatic that may be of independent interest.
متن کاملGrowth functions for Artin monoids
In [S1] we showed that the growth function PM (t) for an Artin monoid of finite type M is a rational function of the form 1/NM (t) where NM (t) is a polynomial1, and gave three conjectures on the denominator polynomial NM (t). In the present note, we remove this assumption on M by showing the result for any type M . Then we give renewed three conjectures on the denominator poynomial NM (t) for ...
متن کاملAn asymmetric generalisation of Artin monoids
We propose a slight weakening of the definitions of Artin monoids and Coxeter monoids. We study one ‘infinite series’ in detail.
متن کاملA poset connected to Artin monoids of simply laced type
Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W -orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representations of the corresponding Artin group A. The poset generalizes many properties of the usual order on positive roots of W given by height. In this paper, a linear representation of the positive monoid of A ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2005
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700035127