  Determining whether two graphs are isomorphic is an important and difficult
problem in graph theory. One way to make progress towards this problem is by
finding and studying graph invariants that distinguish large classes of graphs.
Stanley conjectured that his chromatic symmetric function distinguishes all
trees, which has remained unresolved. Recently, Hasebe and Tsujie introduced an
analogue of Stanley's function for posets, called the strict order
quasisymmetric function, and proved that it distinguishes all rooted trees. In
this paper, we devise a procedure to explicitly reconstruct a rooted tree from
its strict order quasisymmetric function by sampling a finite number of terms.
The procedure not only provides a combinatorial proof of the result of Hasebe
and Tsujie, but also tracks down the representative terms of each rooted tree
that distinguish it from other rooted trees.
