On the minimum size of subset and subsequence sums in integers

@article{Bhanja2021OnTM,
  title={On the minimum size of subset and subsequence sums in integers},
  author={Jagannath Bhanja and Ram Krishna Pandey},
  journal={Comptes Rendus. Math{\'e}matique},
  year={2021}
}
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 α ≤ rk , 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… 
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