Positive $m$-divisible non-crossing partitions and their Kreweras maps
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908411513274368 |
|---|---|
| author | Krattenthaler, Christian Stump, Christian |
| author_facet | Krattenthaler, Christian Stump, Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14996 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positive $m$-divisible non-crossing partitions and their Kreweras maps Krattenthaler, Christian Stump, Christian Combinatorics Representation Theory Primary 20F55, Secondary 05A05 05A10 05A15 05A18 06A07 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. |
| title | Positive $m$-divisible non-crossing partitions and their Kreweras maps |
| topic | Combinatorics Representation Theory Primary 20F55, Secondary 05A05 05A10 05A15 05A18 06A07 |
| url | https://arxiv.org/abs/2506.14996 |