Modul:   MAT591  Discrete mathematics

Parking functions and tree depth

Vortrag von Dr. Amarpreet Rattan

Sprecher eingeladen von: Prof. Dr. Valentin Féray

Datum: 02.02.16  Zeit: 11.15 - 12.15  Raum: Y27H28

Elementary results show that the number of parking functions of length \(n\) is equinumerous with the set of trees on \(n+1\) vertices. Kreweras (1980) showed that further statistics in the two structures are preserved; the number of parking functions with area \(k\) is equinumerous with the number of trees with \(k\) inversions.

In this talk, I will give a further refinement to the above formula and discuss other statistics on parking functions enumerated by the same generating series. I will thoroughly cover the classical results before discussing new ones, so I will not assume any prior knowledge on this topic.