# Ph.D. Thesis

# Publications

- M. Gillespie and J. Levinson. Monodromy and K-theory of Schubert curves via generalized jeu de taquin. Submitted to J. Alg. Comb., 2016.
- M. Gillespie and J. Levinson. Monodromy and K-theory of Schubert curves via generalized jeu de taquin. Extended abstract, FPSAC 2016.
- M. Monks Gillespie. A combinatorial approach to the q,t-symmetry relation in Macdonald polynomials. Accepted for publication modulo revisions in Electronic Journal of Combinatorics.
- K. Monks, K. G. Monks, K. M. Monks, and M. Monks. Strongly sufficient sets and the distribution of arithmetic sequences in the 3x+1 graph. Discrete Mathematics (2013), 468-489.
- M. Monks and K. Ono. Modular forms arising from Q(n) and Dyson's rank. Advances in Applied Mathematics, Dennis Stanton issue (2009). In press.

- M. Monks. Number theoretic properties of generating functions related to Dyson's rank for partitions into distinct parts. Proceedings of the American Mathematical Society
**138** (2010), 481-494.

- M. Monks. Reconstructing permutations from cycle minors. Electronic Journal of Combinatorics
**16** (2009), #R19.

- M. Monks. The solution to the partition reconstruction problem. Journal of Combinatorial Theory, Series A, Vol. 116, Issue 1 (2009).

- M. Monks.
Endomorphisms of the shift dynamical system, discrete derivatives, and applications.
Discrete Mathematics, Vol. 309, Issue 16 (2009), 5196-5205.

# Other miscellaneous papers and writings