Parking functions: What a mathematician thinks of when parking
| Název práce v češtině: | Parkovací funkce aneb problémy parkujícího matematika |
|---|---|
| Název v anglickém jazyce: | Parking functions: What a mathematician thinks of when parking |
| Akademický rok vypsání: | 2023/2024 |
| Typ práce: | diplomová práce |
| Jazyk práce: | angličtina |
| Ústav: | Katedra didaktiky matematiky (32-KDM) |
| Vedoucí / školitel: | doc. RNDr. Antonín Slavík, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 07.01.2024 |
| Datum zadání: | 07.01.2024 |
| Datum potvrzení stud. oddělením: | 08.01.2024 |
| Zásady pro vypracování |
| 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. |
| Seznam odborné literatury |
| 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. |