Problems and results on intersections of product sets and sumsets in semigroups
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911583752421376 |
|---|---|
| author | Nathanson, Melvyn B. |
| author_facet | Nathanson, Melvyn B. |
| contents | For every subset $A$ of a semigroup $S$, let $A^h$ be the set of all products of $h$ elements of $S$. If $(A)_{q\in Q}$ is a family of subsets of $S$, then $A = \bigcap_{q \in Q} A_q$ satisfies $A^h \subseteq \bigcap_{q \in Q} A_q^h$. The product intersection set $H(A_q) = \left\{h \in \mathbf{N}: A^h = \bigcap_{q \in Q} A_q^h \right\}$ is investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04781 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Problems and results on intersections of product sets and sumsets in semigroups Nathanson, Melvyn B. Combinatorics Group Theory Number Theory 11B13, 11B05, 11B75, 11P70, 22D99 For every subset $A$ of a semigroup $S$, let $A^h$ be the set of all products of $h$ elements of $S$. If $(A)_{q\in Q}$ is a family of subsets of $S$, then $A = \bigcap_{q \in Q} A_q$ satisfies $A^h \subseteq \bigcap_{q \in Q} A_q^h$. The product intersection set $H(A_q) = \left\{h \in \mathbf{N}: A^h = \bigcap_{q \in Q} A_q^h \right\}$ is investigated. |
| title | Problems and results on intersections of product sets and sumsets in semigroups |
| topic | Combinatorics Group Theory Number Theory 11B13, 11B05, 11B75, 11P70, 22D99 |
| url | https://arxiv.org/abs/2604.04781 |