Affine permutations and rational slope parking functions
Abstrak
We introduce a new approach to the enumeration of rational slope parking functions with respect to the <mathrm>area</mathrm> and a generalized <mathrm>dinv</mathrm> statistics, and relate the combinatorics of parking functions to that of affine permutations. We relate our construction to two previously known combinatorial constructions: Haglund's bijection ζ exchanging the pairs of statistics (<mathrm>area</mathrm>,<mathrm>dinv</mathrm>) and (<mathrm>bounce</mathrm>, <mathrm>area</mathrm>) on Dyck paths, and Pak-Stanley labeling of the regions of k-Shi hyperplane arrangements by k-parking functions. Essentially, our approach can be viewed as a generalization and a unification of these two constructions.
Topik & Kata Kunci
Penulis (3)
Eugene Gorsky
Mikhail Mazin
Monica Vazirani
Akses Cepat
- Tahun Terbit
- 2014
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2450
- Akses
- Open Access ✓