Toggleability Spaces of Fences
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866929373556244480 |
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| author | Mertin, Alec Poznanović, Svetlana |
| author_facet | Mertin, Alec Poznanović, Svetlana |
| contents | We completely describe the order ideal (resp. antichain) toggleability space for general fences: the space of statistics which are linear combinations of order ideal (antichain) indicator functions and equal to a constant plus a linear combination of toggleability statistics. This allows us to strengthen some homomesies under rowmotion on fences proven by Elizalde et al. and prove some new homomesy results for combinatorial, piecewise-linear, and birational rowmotion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02493 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Toggleability Spaces of Fences Mertin, Alec Poznanović, Svetlana Combinatorics We completely describe the order ideal (resp. antichain) toggleability space for general fences: the space of statistics which are linear combinations of order ideal (antichain) indicator functions and equal to a constant plus a linear combination of toggleability statistics. This allows us to strengthen some homomesies under rowmotion on fences proven by Elizalde et al. and prove some new homomesy results for combinatorial, piecewise-linear, and birational rowmotion. |
| title | Toggleability Spaces of Fences |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.02493 |