A quasisymmetric function in ordered commuting variables 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 
, give its monomial basis. Chromatic
quasisymmetric functions record proper graph colorings
with a statistic depending on the order of the vertices.
