A note on minimal zero-sum sequences over ℤ

Papa A. Sissokho. "A note on minimal zero-sum sequences over ℤ." Acta Arithmetica 166.3 (2014): 279-288. <http://eudml.org/doc/286310>.

@article{PapaA2014,
abstract = {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.},
author = {Papa A. Sissokho},
journal = {Acta Arithmetica},
keywords = {minimal zero-sum sequence; primitive partition identity; Hilbert basis},
language = {eng},
number = {3},
pages = {279-288},
title = {A note on minimal zero-sum sequences over ℤ},
url = {http://eudml.org/doc/286310},
volume = {166},
year = {2014},
}

TY - JOUR
AU - Papa A. Sissokho
TI - A note on minimal zero-sum sequences over ℤ
JO - Acta Arithmetica
PY - 2014
VL - 166
IS - 3
SP - 279
EP - 288
AB - 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.
LA - eng
KW - minimal zero-sum sequence; primitive partition identity; Hilbert basis
UR - http://eudml.org/doc/286310
ER -