Full Grid Lattice Polygons with Maximal Sum of Squares of Edge-Lengths
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909206503751680 |
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| author | Ališauskas, Oliver Mantas Alkauskas, Giedrius Dičiūnas, Valdas |
| author_facet | Ališauskas, Oliver Mantas Alkauskas, Giedrius Dičiūnas, Valdas |
| contents | Consider a subset [1,2,...,n]x[1,2,...,n] of the plane integer lattice. Take any non self-intersecting n^2-gon built on it (straight angles are allowed). The square of a side length is a positive integer. It is thus natural to ask how large the sum of square lengths of such an n^2-gon can be. This maximal value is a new integer sequence, labeled by A358212 in OEIS. In this note we give the lower bound and conjecture that this in fact is the correct answer. We further investigate proper n^2-gons (straight angles are not allowed) and present analogous results. Both sequences (conjecturally) have a different growth size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03011 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Full Grid Lattice Polygons with Maximal Sum of Squares of Edge-Lengths Ališauskas, Oliver Mantas Alkauskas, Giedrius Dičiūnas, Valdas Combinatorics 05A05, 05A15, 05A18 Consider a subset [1,2,...,n]x[1,2,...,n] of the plane integer lattice. Take any non self-intersecting n^2-gon built on it (straight angles are allowed). The square of a side length is a positive integer. It is thus natural to ask how large the sum of square lengths of such an n^2-gon can be. This maximal value is a new integer sequence, labeled by A358212 in OEIS. In this note we give the lower bound and conjecture that this in fact is the correct answer. We further investigate proper n^2-gons (straight angles are not allowed) and present analogous results. Both sequences (conjecturally) have a different growth size. |
| title | Full Grid Lattice Polygons with Maximal Sum of Squares of Edge-Lengths |
| topic | Combinatorics 05A05, 05A15, 05A18 |
| url | https://arxiv.org/abs/2311.03011 |