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 and negative terms . We prove that h ≤ ⌊σ⁺/k⌋ and k ≤ ⌊σ⁺/h⌋, where . 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-3-4,
author = {Papa A. Sissokho},
title = {A note on minimal zero-sum sequences over $\mathbb{Z}$},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {279-288},
zbl = {06373521},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-3-4}
}
Papa A. Sissokho. A note on minimal zero-sum sequences over ℤ. Acta Arithmetica, Tome 166 (2014) pp. 279-288. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-3-4/