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{\bf Ellison-Anne Williams}
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{\bf A Two Parameter Chromatic Symmetric Function}
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We introduce and develop a two-parameter chromatic symmetric function
for a simple graph $G$ over the field of rational functions in $q$ and
$t,\,{\Bbb Q}(q,t)$.  We derive its expansion in terms of the monomial
symmetric functions, $m_{\lambda}$, and present various correlation
properties which exist between the two-parameter chromatic symmetric
function and its corresponding graph.

Additionally, for the complete graph $G$ of order $n$, its
corresponding two-parameter chromatic symmetric function is the
Macdonald polynomial $Q_{(n)}$.  Using this, we develop graphical
analogues for the expansion formulas of the two-row Macdonald
polynomials and the two-row Jack symmetric functions.

Finally, we introduce the ``complement" of this new
function and explore some of its properties.

\bye

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