On Barycentric Constants

Barycentric-sum problems: a survey

Let G be a finite abelian group. A sequence in G is barycentric if it contains one element “average” of its terms. We give a survey of results and open problems concerning sufficient conditions for the existence of barycentric sequences. Moreover values and open problems on the k-barycentric Davenport constant BD(k, G), the barycentric Davenport constant BD(G), the strong k-barycentric Davenpor...

Constrained and generalized barycentric Davenport constants

Let G be a finite abelian group. The constrained barycentric Davenport constant BD(G) with s ≥ 2, is the smallest positive integer d such that every sequence with d terms in G contains a k-barycentric subsequence with 2 ≤ k ≤ s. The generalized barycentric Davenport constant BDs(G), s ≥ 1, is the least positive integer d such that in every sequence with d terms there exist s disjoint barycentri...

Sharp Bounds for Lebesgue Constants of Barycentric Rational Interpolation at Equidistant Points

k-BARYCENTRIC OLSON CONSTANT

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...

Some remarks on barycentric-sum problems over cyclic groups

We 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 {g1, . . . , gk} satisfying g1 + · · ·+ gk = k gj for some 1 ≤ j ≤ k.