The Combinatorics of nabla p_n and connections to the Rational Shuffle Conjecture

Signature Page
Table of Contents
List of Figures
Acknowledgements
Vita
Abstract of the Dissertation
Background and History
A proof of the Square Paths Conjecture
Introduction
Schedules for preference functions
Shifting diagonals and schedules
Dealing with Inverse Descents
A new plethystic symmetric function operator and the Rational Compositional Shuffle Conjecture at t=1/q
Introduction
Commutator properties of our new operators
Polynomiality and positivity.
A parking function setting for our Frobenius characteristics
The action of the operators Du,v on the basis { s[X 1-q ]}
The original proof of Theorem 3.1.1 by the partial fraction method
A new interpretation of pn
Symmetric function identities
A refinement and a conjecture
A special case
Bibliography