Holey Hyperbolic Polyforms
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915874412167168 |
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| author | Eldridge, Summer Prabha, Adithya Roger, Aiden Roger, Cooper Roldán, Érika Toalá-Enríquez, Rosemberg |
| author_facet | Eldridge, Summer Prabha, Adithya Roger, Aiden Roger, Cooper Roldán, Érika Toalá-Enríquez, Rosemberg |
| contents | A polyform is a planar figure formed by gluing congruent regular polygons along entire edges. We study polyforms in hyperbolic ${p,q}$-tessellations and the extremal problem of minimizing the number of tiles needed to realize exactly $h$ holes. Denoting this minimum by $g_{p,q}(h)$, we establish general lower and upper bounds, compute exact values in several small cases, and give a sufficient structural condition for a polyform to have $h$ holes and $g_{p,q}(h)$ tiles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18638 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Holey Hyperbolic Polyforms Eldridge, Summer Prabha, Adithya Roger, Aiden Roger, Cooper Roldán, Érika Toalá-Enríquez, Rosemberg Combinatorics Algebraic Topology 05A20, 05B50, 05C07, 05C10, 52C20, 05C35, 51M10, 52A40, 49Q10 A polyform is a planar figure formed by gluing congruent regular polygons along entire edges. We study polyforms in hyperbolic ${p,q}$-tessellations and the extremal problem of minimizing the number of tiles needed to realize exactly $h$ holes. Denoting this minimum by $g_{p,q}(h)$, we establish general lower and upper bounds, compute exact values in several small cases, and give a sufficient structural condition for a polyform to have $h$ holes and $g_{p,q}(h)$ tiles. |
| title | Holey Hyperbolic Polyforms |
| topic | Combinatorics Algebraic Topology 05A20, 05B50, 05C07, 05C10, 52C20, 05C35, 51M10, 52A40, 49Q10 |
| url | https://arxiv.org/abs/2603.18638 |