EXISTENCE CONDITIONS FOR k-BARYCENTRIC OLSON CONSTANT
2020 ◽
Vol 28
(1)
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pp. 39-53
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Let (G, +) be a finite abelian group and 3 ≤ k ≤ |G| a positive integer. The k-barycentric Olson constant denoted by BO(k, G) is defined as the smallest integer ℓ such that each set A of G with |A| = ℓ contains a subset with k elements {a1, . . . , ak} satisfying a1 + · · · + ak = kaj for some 1 ≤ j ≤ k. We establish some general conditions on G assuring the existence of BO(k, G) for each 3 ≤ k ≤ |G|. In particular, from our results we can derive the existence conditions for cyclic groups and for elementary p-groups p ≥ 3. We give a special treatment over the existence condition for the elementary 2-groups.
1981 ◽
Vol 33
(4)
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pp. 817-825
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1960 ◽
Vol 12
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pp. 447-462
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2011 ◽
Vol 12
(01n02)
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pp. 125-135
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2017 ◽
Vol 14
(01)
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pp. 167-191
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2001 ◽
Vol 63
(1)
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pp. 115-121
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2017 ◽
Vol 13
(02)
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pp. 301-308
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2016 ◽
Vol 101
(3)
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pp. 310-334
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