A quasisymmetric function in ordered commuting variables 
over a field is a formal
power series of bounded total degree whose coefficient of 
,
for 
, depends only on the positive
integers 
, ..., 
.
It need not be invariant under arbitrary permutations
of the variables. For example,
 |
is quasisymmetric but is not symmetric. The functions 
, indexed by compositions 
, together with the constant 1 give a monomial basis. Chromatic
quasisymmetric functions record proper colorings
with a statistic depending on the order of the vertices.
