My research is in combinatorics and discrete probability. In particular, I am interested in permutations and parking functions, and combinatorial probability (mainly random walks and related topics). Below is my list of publications.

Publications

Preprint

See also the list of my preprints at arXiv.

1. A parking function analog of the Schröder numbers. Lucy Martinez and Doron Zeilberger.
   [arXiv] [Maple packages] [OEIS sequence]
2. Automatic enumeration of tilings by polyominoes. Lucy Martinez.
   [arXiv] [GitHub]
3. Lehmer parking functions and their outcomes. Melissa Beerbower, Jennifer Elder, Pamela E. Harris, Ilana Lavene, Lucy Martinez, Adam Martinson, and Molly Oldham.
   [arXiv]
4. How many coin tosses would you need until you get n heads or m tails? Svante Janson , Lucy Martinez, and Doron Zeilberger.
   [arXiv] [Maple package]
5. Enumerating vector parking functions and their outcomes based on specified lucky cars. Melanie Ferreri, Pamela E. Harris, Lucy Martinez, and Eric Swartz.
   [arXiv]



Accepted/In Press

1. Lucky cars in Fubini rankings and unit Fubini rankings. Camilo Barreto, Melissa Beerbower, Jennifer Elder, Pamela E. Harris, Lucy Martinez, José L. Ramírez, Samuel Ramírez, Grant Shirley, and Julio C. Vásquez. To appear in Studia Scientiarum Mathematicarum Hungarica.
   [arXiv]



Published

1. Parking functions with a fixed set of lucky cars. Pamela E. Harris and Lucy Martinez. Bulletin of the Institute of Combinatorics and its Applications, Vol. 108 (2026), 104-150. (abstract).
   [journal link] [arXiv]
2. A symbolic computational approach to the generalized gambler's ruin problem in one and two dimensions. Lucy Martinez. Journal of Difference Equations and Applications, Vol. 32 (2026), no. 3, 387-411.
   [journal link] [arXiv] [GitHub]
3. Primeness of generalized parking functions. Sam Armon, Joanne Beckford, Dillon Hanson, Naomi Krawzik, Olya Mandelshtam, Lucy Martinez, and Catherine Yan. The Electronic Journal of Combinatorics, Vol. 32 (2025), no. 4, P4.48.
   [journal link] [arXiv]
4. Hitting k primes by dice rolls. Noga Alon, Yaakov Malinovsky, Lucy Martinez, and Doron Zeilberger. The Electronic Journal of Combinatorics, Vol. 32 (2025), no. 4, P4.16.
   [journal link] [arXiv] [Maple package] [News article]
5. Pullback parking functions. Jennifer Elder, Pamela E. Harris, Lybitina Koene, Ilana Lavene, Lucy Martinez, and Molly Oldham. American Journal of Combinatorics, Vol 4 (2025), 1-22.
   [journal link ] [arXiv]
6. A guide to the risk-averse gambler and resolving the St. Petersburg paradox once and for all. Lucy Martinez and Doron Zeilberger. The College of Mathematics Journal, Vol 55 (2024), no. 3, 226-234.
   [journal link] [arXiv] [Maple package]
7. Repetitions of Pak-Stanley labels in G-Shi arrangements. Cara Bennett, Lucy Martinez, Ava Mock, Gordon Rojas Kirby, and Roshni Truax. Discrete Mathematics, Vol. 347 (2024), no. 9.
   [journal link] [arXiv]
8. On Kostant’s weight q-multiplicity formula for sl_4(C). Rebecca. E. Garcia, Pamela E. Harris, Marissa Loving, Lucy Martinez, David Melendez, Joseph Rennie, Gordon Rojas Kirby, and Daniel Tinoco. Applicable Algebra in Engineering, Communication and Computing, Vol. 33 (2022), no. 4, 353-418.
   Received award for 2022 Best Paper in AAECC! [ link ]
   [journal link] [arXiv]

Expository Writing

1. How many dice rolls would it take to reach your favorite kind of number? Lucy Martinez and Doron Zeilberger. Maple Transactions, Vol 3 (2023), no. 3, Article 15953.
   [journal link] [arXiv] [Maple package] [OEIS sequence]