The Shareshian-Wachs conjecture asserts elementary positivity, together with unimodality, for chromatic quasisymmetric functions
of natural unit interval graphs. Such
a graph on ![[n]](/images/equations/Shareshian-WachsConjecture/Inline1.svg)
is specified by weakly increasing integers 
,
..., 
with 
,
using edges 
for 
. Its elementary-basis expansion is
 |
where 
.
Elementary positivity requires ![c_lambda(q) in N[q]](/images/equations/Shareshian-WachsConjecture/Inline8.svg)
. Unimodality further requires each coefficient
sequence to increase and then decrease.
