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- W1978935638 abstract "Let $A={a_0,a_1,ldots,a_{k-1}}$ be a set of $k$ integers. For any integer $hge 1$ 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." @default.
- W1978935638 created "2016-06-24" @default.
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- W1978935638 date "2015-07-01" @default.
- W1978935638 modified "2023-09-23" @default.
- W1978935638 title "On the cardinality of general <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mi>h</mml:mi></mml:math>-fold sumsets" @default.
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- W1978935638 doi "https://doi.org/10.1016/j.ejc.2015.02.002" @default.
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