Type C parking functions and a zeta map
Robin Sulzgruber, Marko Thiel
TL;DR
This paper introduces type C parking functions, establishes a bijection with Shi arrangement regions, and generalizes the zeta map to relate dinv' and area' statistics.
Contribution
It defines type C parking functions and constructs a natural analogue of the zeta map linking dinv' and area' statistics.
Findings
Bijection between type C parking functions and Shi arrangement regions
Three descriptions of the generalized zeta map
Mapping dinv' to area' statistic in type C setting
Abstract
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.
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