Additive sumset sizes with tetrahedral differences
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909756681093120 |
|---|---|
| author | Nathanson, Melvyn B. |
| author_facet | Nathanson, Melvyn B. |
| contents | Experimental calculations suggest that the $h$-fold sumset sizes of 4-element sets of integers are concentrated at $h$ numbers that are differences of tetrahedral numbers. In this paper it is proved that these "popular" sumset sizes always exist. Explicit $h$-adically defined sets are constructed for each of these numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Additive sumset sizes with tetrahedral differences Nathanson, Melvyn B. Number Theory Combinatorics 11B13, 11B05, 11B75, 11P70, 11Y16, 11Y55 Experimental calculations suggest that the $h$-fold sumset sizes of 4-element sets of integers are concentrated at $h$ numbers that are differences of tetrahedral numbers. In this paper it is proved that these "popular" sumset sizes always exist. Explicit $h$-adically defined sets are constructed for each of these numbers. |
| title | Additive sumset sizes with tetrahedral differences |
| topic | Number Theory Combinatorics 11B13, 11B05, 11B75, 11P70, 11Y16, 11Y55 |
| url | https://arxiv.org/abs/2507.08646 |