k-BARYCENTRIC OLSON CONSTANT
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چکیده
Let G be a finite Abelian group of order n. A k-sequence in G is said to be barycentric if it contains an element which is the “average” of its terms. The kbarycentric Olson constant BO(k, G) is introduced as the minimal positive integer t such that any t-set in G contains a k-barycentric set. Conditions for the existence of BO(k, G) are established and some values or bounds are given. Moreover, new values for the k-barycentric Davenport constant BD(k, G) and barycentric Ramsey numbers for stars BR(K1,k, G) are given. These constants, defined in some of our previous works, use sequences instead of sets.
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تاریخ انتشار 2009