A Kazhdan-Lusztig polynomial 
is a polynomial associated
with two elements 
in the Bruhat order
of a Coxeter group. In the equal-parameter convention,
these polynomials give the coefficients
of the canonical basis of its Hecke algebra in the
standard basis. They have integer coefficients,
,
and
 |
when 
,
where 
is Coxeter length. For example, a Bruhat interval of length one has 
. The combinatorial
invariance conjecture asks whether its abstract partially
ordered set determines 
.
