Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.06806 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911379912392704 |
|---|---|
| author | Bui, Vuong |
| author_facet | Bui, Vuong |
| contents | We provide a short and elementary proof that the growth constant of polyiamonds is at most $1+2z+3z^2$ for the unique real root $z$ of the equation $2z^3+z^2-1=0$. This coincidentally suffices to recover the best known upper bound $3.6108$. Unlike the previous proof of this bound, which relied on computer-assisted technical arguments and the counts of polyiamonds with up to 75 triangles, our method is based on a straightforward recurrence that can be verified by hand with minimal effort. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06806 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A short proof of an upper bound on the growth constant of polyiamonds Bui, Vuong Combinatorics We provide a short and elementary proof that the growth constant of polyiamonds is at most $1+2z+3z^2$ for the unique real root $z$ of the equation $2z^3+z^2-1=0$. This coincidentally suffices to recover the best known upper bound $3.6108$. Unlike the previous proof of this bound, which relied on computer-assisted technical arguments and the counts of polyiamonds with up to 75 triangles, our method is based on a straightforward recurrence that can be verified by hand with minimal effort. |
| title | A short proof of an upper bound on the growth constant of polyiamonds |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.06806 |