• Corpus ID: 209367665

A nullstellensatz for sequences over F_p

@inproceedings{Balandraud2021ANF,
  title={A nullstellensatz for sequences over F\_p},
  author={{\'E}ric Balandraud and Benjamin Girard},
  year={2021}
}
. Let p be a prime and let A = ( a 1 ,...,a ℓ ) be a sequence of nonzero elements in F p . In this paper, we study the set of all 0-1 solutions to the equation a 1 x 1 + ··· + a ℓ x ℓ = 0 . We prove that whenever ℓ > p , this set actually characterizes A up to a nonzero multiplicative constant, which is no longer true for ℓ < p . The critical case ℓ = p is of particular interest. In this context, we prove that whenever ℓ = p and A is nonconstant, the above equation has at least p − 1 minimal 0… 

Representing Sequence Subsums as Sumsets of Near Equal Sized Sets

  • D. Grynkiewicz
  • Mathematics
    Springer Proceedings in Mathematics & Statistics
  • 2021
For a sequence $S$ of terms from an abelian group $G$ of length $|S|$, let $\Sigma_n(S)$ denote the set of all elements that can be represented as the sum of terms in some $n$-term subsequence of

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