التفاصيل البيبلوغرافية
| العنوان: |
Periodic triangulations of $\mathbb{Z}^n$ |
| المؤلفون: |
Sikirić, Mathieu Dutour, Garber, Alexey |
| المصدر: |
Electronic J. Comb, 27:2 (2020), P2.36 |
| سنة النشر: |
2018 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Combinatorics, Mathematics - Metric Geometry |
| الوصف: |
We consider in this work triangulations of $\mathbb{Z}^n$ that are periodic along $\mathbb{Z}^n$. They generalize the triangulations obtained from Delaunay tessellations of lattices. Other important property is the regularity and central-symmetry property of triangulations. Full enumeration for dimension at most $4$ is obtained. In dimension $5$ several new phenomena happen: there are centrally-symmetric triangulations that are not Delaunay, there are non-regular triangulations (it could happen in dimension $4$) and a given simplex has a priori an infinity of possible adjacent simplices. We found $950$ periodic triangulations in dimension $5$ but finiteness is unknown. |
| نوع الوثيقة: |
Working Paper |
| DOI: |
10.37236/8298 |
| URL الوصول: |
http://arxiv.org/abs/1810.10911 |
| رقم الانضمام: |
edsarx.1810.10911 |
| قاعدة البيانات: |
arXiv |