Let 
be an integer such that 
, where 
is a partition
of 
if 
,
where 
are a sequence of positive integers stabilizing 0 such that 
. Also let 
be the number of parts of 
of size 
. Then the permutation 
,
where 
is the symmetric group, acts on the variables 
, ..., 
by sending 
to 
. Letting 
be a complex number, the
Hall-Littlewood polynomials are defined by
 |
These polynomials interpolate between the Schur functions (with 
) and the monomial symmetric functions (with 
; Fulman 1999).
