The minimum length of an axis-aligned rectangular tiling of a flat torus
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914370190049280 |
|---|---|
| author | Lin, Hau-Yi Lin, Wu-Hsiung Chang, Gerard Jennhwa |
| author_facet | Lin, Hau-Yi Lin, Wu-Hsiung Chang, Gerard Jennhwa |
| contents | A flat torus is the quotient of the Euclidean plane over a lattice generated by a basis, and an axis-aligned rectangular tiling of a flat torus is a partition into finitely many rectangles whose sides are axis-aligned. We provide the minimum sum of the perimeter of rectangles for an axis-aligned rectangular tiling, and prove that it is attainable by either exactly one rectangle or exactly two rectangles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04765 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The minimum length of an axis-aligned rectangular tiling of a flat torus Lin, Hau-Yi Lin, Wu-Hsiung Chang, Gerard Jennhwa Combinatorics 05B45, 52C20 A flat torus is the quotient of the Euclidean plane over a lattice generated by a basis, and an axis-aligned rectangular tiling of a flat torus is a partition into finitely many rectangles whose sides are axis-aligned. We provide the minimum sum of the perimeter of rectangles for an axis-aligned rectangular tiling, and prove that it is attainable by either exactly one rectangle or exactly two rectangles. |
| title | The minimum length of an axis-aligned rectangular tiling of a flat torus |
| topic | Combinatorics 05B45, 52C20 |
| url | https://arxiv.org/abs/2603.04765 |