\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Henrik Eriksson and Kimmo Eriksson}
%
%
\medskip
\noindent
%
%
{\bf Words with Intervening Neighbours in Infinite Coxeter Groups are Reduced}
%
%
\vskip 5mm
\noindent
%
%
%
%
Consider a graph with vertex set $S$. A word in the alphabet $S$ has
the intervening neighbours property if any two occurrences of
the same letter are separated by all its graph neighbours.
For a Coxeter graph, words represent group elements. Speyer recently proved 
that words with the intervening neighbours property are reduced if the 
group is infinite and irreducible. We present a new and shorter proof using 
the root automaton for recognition of reduced words.



\bye