## Sulzgruber, Robin and Thiel, Marko - Type C parking functions and a zeta map

dmtcs:2496 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Type C parking functions and a zeta map

Authors: Sulzgruber, Robin and Thiel, Marko

We introduce type $C$ parking functions, encoded as vertically labelled lattice paths and endowed with a statistic dinv'. We define a bijection from type $C$ parking functions to regions of the Shi arrangement of type $C$, encoded as diagonally labelled ballot paths and endowed with a natural statistic area'. This bijection is a natural analogue of the zeta map of Haglund and Loehr and maps dinv' to area'. We give three different descriptions of it.

Source : oai:HAL:hal-01337800v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: parking functions,Shi arrangement,zeta map,dinv statistic,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]