Nelsen K.A. A New Interpretation of the Cocharge Statistic

Old Main: University of Pennsylvania, 2005. — 64 p.In this thesis we will start by introducing the combinatorial formula for the Macdonald polynomial. We then show how cocharge arises naturally from this formula. Expanding these methods to compositions, we see how an alternative description of cocharge arises naturally from the combinatorial statistics used in the formula for the Macdonald polynomial. The final chapter of the thesis outlines the proof of Lascoux and Sch¨utzenberger’s famous theorem that expands the Kostka-Foulkes polynomial in terms of charge.