Gorsky, Eugene and Mazin, Mikhail and Vazirani, Monica - Affine permutations and rational slope parking functions

dmtcs:2450 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Affine permutations and rational slope parking functions

Authors: Gorsky, Eugene and Mazin, Mikhail and Vazirani, Monica

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.


Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Submitted on: November 21, 2016
Keywords: Parking functions,affine permutations,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]


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