2013
DOI: 10.1016/j.ejc.2013.05.025
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Abstract: International audienceWe derive some new results on the k-th barycentric Olson constants of abelian groups (mainly cyclic). This quantity, for a finite abelian (additive) group (G,+), is defined as the smallest integer l such that each subset A of G with at least l elements contains a subset with k elements {g_1, ... , g_k} satisfying g_1 + ... + g_k = k g_j for some 1 <= j <= k

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Cited by 1 publication
(2 citation statements)
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References 15 publications
(24 reference statements)
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“…Existence conditions of the k-barycentric Olson constant with 3 ≤ k ≤ |G| were initially considered in [14] with the study on cyclic groups using the Orbits Theory. In [13] Ordaz, Plagne and Schmid researched on the existence conditions of BO(k, G) with |G| − 2 ≤ k ≤ |G| over finite abelian groups G in general; their results were Lemma 1 and Proposition 1. In case there are no k-barycentric sets in G we write BO(k, G) = |G| + 1.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Existence conditions of the k-barycentric Olson constant with 3 ≤ k ≤ |G| were initially considered in [14] with the study on cyclic groups using the Orbits Theory. In [13] Ordaz, Plagne and Schmid researched on the existence conditions of BO(k, G) with |G| − 2 ≤ k ≤ |G| over finite abelian groups G in general; their results were Lemma 1 and Proposition 1. In case there are no k-barycentric sets in G we write BO(k, G) = |G| + 1.…”
Section: Introductionmentioning
confidence: 99%
“…[13] ,Lemma 3.1) Let G be a finite abelian group. Then σ(G) = { b * if r 2 (G) = 1 and b * denote the only element with order 2, 0 in other case.…”
mentioning
confidence: 99%