Partial Alternating Sign Matrix Bijections and Dynamics
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910353344954368 |
|---|---|
| author | Heuer, Dylan |
| author_facet | Heuer, Dylan |
| contents | We investigate analogues of alternating sign matrices, called partial alternating sign matrices. We prove bijections between these matrices and several other combinatorial objects. We use an analogue of Wieland's gyration on fully-packed loops, which we relate to the study of toggles and order ideals. Finally, we show that rowmotion on order ideals of a certain poset and gyration on partial fully-packed loop configurations are in equivariant bijection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02242 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial Alternating Sign Matrix Bijections and Dynamics Heuer, Dylan Combinatorics 05A05 We investigate analogues of alternating sign matrices, called partial alternating sign matrices. We prove bijections between these matrices and several other combinatorial objects. We use an analogue of Wieland's gyration on fully-packed loops, which we relate to the study of toggles and order ideals. Finally, we show that rowmotion on order ideals of a certain poset and gyration on partial fully-packed loop configurations are in equivariant bijection. |
| title | Partial Alternating Sign Matrix Bijections and Dynamics |
| topic | Combinatorics 05A05 |
| url | https://arxiv.org/abs/2403.02242 |