A reduced word, in the construction of a free group, is a finite word in an alphabet
of generators and their formal inverses that
contains no consecutive inverse pair 
or 
. Repeatedly deleting these pairs gives a unique reduced
word, possibly empty (Milne 2025, pp. 32-33).
In a Coxeter group 
, using the group generators 
of its defining Coxeter group
presentation, a reduced word for 
is an expression 
, with 
, having the least possible number of letters.
This is the convention used in the subword property for
the Bruhat order (Björner and Brenti 2005, p. 15).
