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- W4301400600 abstract "Let $mathcal{A}$ be a finite sequence of $rk$ terms which is made up of $k$ distinct integers each appearing exactly $r$ times in $mathcal{A}$. The sum of all terms of a subsequence of $mathcal{A}$ is called a subsequence sum of $mathcal{A}$. For a fixed nonnegative integer $alpha leq rk$, let $Sigma_{alpha} (r,mathcal{A})$ be the set of all subsequence sums of $mathcal{A}$ that correspond to the subsequences of length $alpha$ or more. When $r=1$, we call the set of subsequence sums as the set of subset sums and we denote it by $Sigma_{alpha} (A)$ instead of $Sigma_{alpha} (1,mathcal{A})$. In this article, we give optimal lower bounds for the sizes of $Sigma_{alpha} (A)$ and $Sigma_{alpha} (r,mathcal{A})$. As special cases, we also obtain some already known results in this study." @default.
- W4301400600 created "2022-10-05" @default.
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- W4301400600 date "2021-08-16" @default.
- W4301400600 modified "2023-09-29" @default.
- W4301400600 title "On the minimum size of subset and subsequence sums in integers" @default.
- W4301400600 doi "https://doi.org/10.48550/arxiv.2108.07042" @default.
- W4301400600 hasPublicationYear "2021" @default.
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