# Permutahedral matchings, zonotopal tilings, and d-partitions

Time: 10:30 -- Location: Salle Philippe Flajolet du LIX

In this talk I will present higher dimensional generalizations of the following three concepts:

- (a) perfect matchings of a hexagonal tiling,
- (b) rhombus tilings of a hexagon, and
- (c) plane partitions.

I will show that these generalizations are equivalent under certain specific bijections. The generalizations of (b) and (c) have been already studied in the literature but, as far as I know, the generalization of (a) appears to be new. This is work in progress based on discussions with Tomack Gilmore and Vivien Ripoll.