2021
DOI: 10.48550/arxiv.2111.05394
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Zero-sum partitions of Abelian groups of order $2^n$

Abstract: The following problem has been known since the 80's. Let Γ be an Abelian group of order m (denoted |Γ| = m), and let t and m i , 1 ≤ i ≤ t, be positive integers such thatIt was shown that the condition m i ≥ 2 (for any i, 24,31]), where I(Γ) is the set of involutions of Γ. In this paper we show that the condition m i ≥ 3 is sufficient for Γ such that |I(Γ)| > 1 and |Γ| = 2 n for any positive integer n. * This work was partially supported by the Faculty of Applied Mathematics AGH UST statutory tasks within subs… Show more

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(2 citation statements)
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“…Notice that Corollary 3.8 extends the results on Γ-distance magic labelings of complete k-partite graphs presented in [5].…”
Section: Magic and Anti-magic Labeling In Graphs With Twinssupporting
confidence: 76%
See 1 more Smart Citation
“…Notice that Corollary 3.8 extends the results on Γ-distance magic labelings of complete k-partite graphs presented in [5].…”
Section: Magic and Anti-magic Labeling In Graphs With Twinssupporting
confidence: 76%
“…, where w i = 0 for all i, 1 ≤ i ≤ t). In [5], we generalized this condition with the following definition. Definition 1.3.…”
Section: Main Problemmentioning
confidence: 99%