Positive
m-divisible non-crossing partitions and their Kreweras maps
(169 pages)
Abstract.
We study positive m-divisible non-crossing partitions and their positive Kreweras maps.
In classical types, we describe their combinatorial realisations as certain non-crossing set partitions.
We also realise these positive Kreweras maps as pseudo-rotations on a circle, respectively on an annulus.
We enumerate positive m-divisible non-crossing partitions in classical types that are invariant under powers of the
positive Kreweras maps with respect to several parameters.
In order to cope with the exceptional types, we develop a different combinatorial model in general type describing positive m-divisible non-crossing partitions that are invariant under powers of the positive Kreweras maps.
We finally show that altogether these results establish several cyclic sieving phenomena.
The following versions are available:
Back to Christian Krattenthaler's
home page.