Parking functions: What a mathematician thinks of when parking

• Thesis title in Czech: Parkovací funkce aneb problémy parkujícího matematika
• Thesis title in English: Parking functions: What a mathematician thinks of when parking
• Academic year of topic announcement: 2023/2024
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Department of Mathematics Education (32-KDM)
• Supervisor: doc. RNDr. Antonín Slavík, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 07.01.2024
• Date of assignment: 07.01.2024
• Confirmed by Study dept. on: 08.01.2024

Guidelines

The thesis will provide a survey of the concept of a parking function, its numerous extensions and generalizations. It will also focus on the relations between (generalized) parking functions and other combinatorial or algebraic objects (e.g., Dyck paths). The student is expected to think about open conjectures in this area, and possibly formulate and solve new problems.

References

C. H. Yan: Parking functions. In M. Bóna (ed.): Handbook of Enumerative Combinatorics. CRC Press, 2015, 835–893.
R. Ehrenborg, A. Happ: Parking cars of different sizes. Amer. Math. Monthly. 123 (2016), 1045–1048.
E. Colaric, R. DeMuse, J. L. Martin, Mei Yin: Interval parking functions. Adv. Appl. Math. 123 (2021), article no. 102129.
L. Colmenarejo, P. E. Harris, Z. Jones, C. Keller, A. Ramos Rodríguez, E. Sukarto, A. R. Vindas-Meléndez: Counting k-Naples parking functions through permutations and the k-Naples area statistic. Enumer. Comb. Appl. 1 (2021), No. 2, Article ID S2R11.
J. Carlson, A. Christensen, P. E. Harris, Z. Jones, A. Ramos Rodríguez: Parking functions: choose your own adventure. Coll. Math. J. 52 (2021), 254–264.
A. Christensen, P. E. Harris, Z. Jones, M. Loving, A. Ramos Rodríguez, J. Rennie, G. Rojas Kirby: A generalization of parking functions allowing backward movement. Electron. J. Comb. 27 (2020), article no. P1.33.