Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On the cardinality of general $h$-fold sumsets (1406.7346v1)

Published 28 Jun 2014 in math.NT and math.CO

Abstract: Let $A={a_0,a_1,\ldots,a_{k-1}}$ be a set of $k$ integers. For any integer $h\ge 1$ and any ordered $k$-tuple of positive integers $\mathbf{r}=(r_0,r_1,\ldots,r_{k-1})$, we define a general $h$-fold sumset, denoted by $h{(\mathbf{r})}A$, which is the set of all sums of $h$ elements of $A$, where $a_i$ appearing in the sum can be repeated at most $r_i$ times for $i=0,1,\ldots,k-1$. In this paper, we give the best lower bound for $|h{(\mathbf{r})}A|$ in terms of $\mathbf{r}$ and $h$ and determine the structure of the set $A$ when $|h{(\mathbf{r})}A|$ is minimal. This generalizes results of Nathanson, and recent results of Mistri and Pandey and also solves a problem of Mistri and Pandey.

Summary

We haven't generated a summary for this paper yet.