Dimensions of toggleability spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908496729997312 |
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| author | Adenbaum, Ben Daugherty, Spencer Mayers, Nicholas |
| author_facet | Adenbaum, Ben Daugherty, Spencer Mayers, Nicholas |
| contents | We establish a conjecture of Defant, Hopkins, Poznanović, and Propp concerning the dimensions of toggleability spaces for products of chains, shifted staircases, type-A root posets, and type-B posets. Generalizing this result, we show that for a larger family of posets defined by restricted diagrams, the dimensions of toggleability spaces are equal to the rank of the poset plus one. As part of our approach, we build upon the technique of rook statistics introduced by Chan, Haddadan, Hopkins, and Moci. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_14974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimensions of toggleability spaces Adenbaum, Ben Daugherty, Spencer Mayers, Nicholas Combinatorics 05E18, 06A07 We establish a conjecture of Defant, Hopkins, Poznanović, and Propp concerning the dimensions of toggleability spaces for products of chains, shifted staircases, type-A root posets, and type-B posets. Generalizing this result, we show that for a larger family of posets defined by restricted diagrams, the dimensions of toggleability spaces are equal to the rank of the poset plus one. As part of our approach, we build upon the technique of rook statistics introduced by Chan, Haddadan, Hopkins, and Moci. |
| title | Dimensions of toggleability spaces |
| topic | Combinatorics 05E18, 06A07 |
| url | https://arxiv.org/abs/2508.14974 |