Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

A note on minimal zero-sum sequences over ℤ

100%

Sissokho P.

Acta Arithmetica

2014

tom 166

nr 3

279-288

A zero-sum sequence over ℤ is a sequence with terms in ℤ that sum to 0. It is called minimal if it does not contain a proper zero-sum subsequence. Consider a minimal zero-sum sequence over ℤ with positive terms $a₁,...,a_{h}$ and negative terms $b₁,...,b_{k}$. We prove that h ≤ ⌊σ⁺/k⌋ and k ≤ ⌊σ⁺/h⌋, where $σ⁺ = ∑_{i=1}^{h} a_{i} = -∑_{j=1}^{k} b_{j}$. These bounds are tight and improve upon previous results. We also show a natural partial order structure on the collection of all minimal zero-sum sequences over the set {i∈ ℤ : -n ≤ i ≤ n} for any positive integer n.

Ograniczanie wyników

1 Acta Arithmetica

1 Sissokho P.

1 2014

Wyniki wyszukiwania

A note on minimal zero-sum sequences over ℤ