Comptes Rendus
Combinatorics, Number theory
On the minimum size of subset and subsequence sums in integers
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1099-1111.

Let 𝒜 be a sequence of rk terms which is made up of k distinct integers each appearing exactly r times in 𝒜. The sum of all terms of a subsequence of 𝒜 is called a subsequence sum of 𝒜. For a nonnegative integer αrk, let Σ α (𝒜) be the set of all subsequence sums of 𝒜 that correspond to the subsequences of length α or more. When r=1, we call the subsequence sums as subset sums and we write Σ α (A) for Σ α (𝒜). In this article, using some simple combinatorial arguments, we establish optimal lower bounds for the size of Σ α (A) and Σ α (𝒜). As special cases, we also obtain some already known results in this study.

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DOI: 10.5802/crmath.361
Classification: 11B75, 11B13, 11B30
Jagannath Bhanja 1; Ram Krishna Pandey 2

1 Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute, Chhatnag Road, Jhunsi, Prayagraj-211019, India
2 Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Jagannath Bhanja; Ram Krishna Pandey. On the minimum size of subset and subsequence sums in integers. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1099-1111. doi : 10.5802/crmath.361. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.361/

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