A note on minimal zero-sum sequences over ℤ

• Autorzy: Papa A. Sissokho
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11B75: Other combinatorial number theory
• 11P70: Inverse problems of additive number theory, including sumsets
• 11B30: Arithmetic combinatorics; higher degree uniformity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 166
• Numer: 3
• Strony: 279-288

Daty

wydano

2014

Twórcy

autor

Papa A. Sissokho

• Mathematics Department, Illinois State University, Normal, IL 61790-4520, U.S.A.

Identyfikatory

DOI

10.4064/aa166-3-4