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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.16598 |
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| _version_ | 1866908601175506944 |
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| author | Solotko, Saskia Tung, Katherine Yang, Mengyuan Zhang, Yuchong |
| author_facet | Solotko, Saskia Tung, Katherine Yang, Mengyuan Zhang, Yuchong |
| contents | We prove that the simplicial complex $Δ_{\mathcal{C}_n,2}$ is pure and a weak pseudomanifold of dimension $2(n-1)$, where $Δ_{\mathcal{C}_n,2}$ is the simplicial complex associated with $2$-triangulations on the half-cylinder with $n$ marked points. This result generalizes the work of Vincent Pilaud and Francisco Santos for polygons and resolves a conjecture of Mathias Lepoutre and Vincent Pilaud for $k=2$. To achieve this, we show that $2$-triangulations on the half-cylinder decompose as complexes of star polygons, and that $2$-triangulations on the half-cylinder are in bijection with $2$-triangulations on the $4n$-gon invariant under rotation by $π/2$ radians. Building on work by Vincent Pilaud and Christian Stump, we also introduce chevron pipe dreams, a new combinatorial model that more naturally captures the symmetries of $k$-triangulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multitriangulations on the half-cylinder Solotko, Saskia Tung, Katherine Yang, Mengyuan Zhang, Yuchong Combinatorics We prove that the simplicial complex $Δ_{\mathcal{C}_n,2}$ is pure and a weak pseudomanifold of dimension $2(n-1)$, where $Δ_{\mathcal{C}_n,2}$ is the simplicial complex associated with $2$-triangulations on the half-cylinder with $n$ marked points. This result generalizes the work of Vincent Pilaud and Francisco Santos for polygons and resolves a conjecture of Mathias Lepoutre and Vincent Pilaud for $k=2$. To achieve this, we show that $2$-triangulations on the half-cylinder decompose as complexes of star polygons, and that $2$-triangulations on the half-cylinder are in bijection with $2$-triangulations on the $4n$-gon invariant under rotation by $π/2$ radians. Building on work by Vincent Pilaud and Christian Stump, we also introduce chevron pipe dreams, a new combinatorial model that more naturally captures the symmetries of $k$-triangulations. |
| title | Multitriangulations on the half-cylinder |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.16598 |