We show that two classes of combinatorial objectsâ€“inversion tables with no subsequence of decreasing consecutive numbers and matchings with no 2-nestingsâ€“are enumerated by the Fishburn numbers. Inâ€¦ (More)

We examine the q = 1 and t = 0 special cases of the parking functions conjecture. The parking functions conjecture states that the Hilbert series for the space of diagonal harmonics is equal to theâ€¦ (More)

We show how the generating function for signed Stirling numbers of the first kind can be proved using the involution principle and a natural combinatorial interpretation based on cycle-coloredâ€¦ (More)

We describe proofs of the standard generating formulas for unsigned and signed Stirling numbers of the first kind that follow from a natural combinatorial interpretation based on cycle-coloredâ€¦ (More)

COMBINATORIAL STRUCTURES AND GENERATING FUNCTIONS OF FISHBURN NUMBERS, PARKING FUNCTIONS, AND TESLER MATRICES. Paul Levande James Haglund This dissertation reflects the authorâ€™s work on two problemsâ€¦ (More)