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...

This paper suggests that the measurement of error between mesh surfaces that are similar can be performed more time-efficiently than the existing methods offer. We presume that evaluation of error between similar surfaces does not require so many sample points and two-way distance measurement. Also we apply a different technique for sample point picking that involves barycentric coordinates. Te...

With a plethora of available classification performance measures, choosing the right metric for the right task requires careful thought. However, analyzing measures with respect to complete ranges of their values is a difficult and challenging task. In this study, we attempt to support such analyses with a specialized visualization technique, which operates in a barycentric coordinate system us...

We study face vectors of barycentric subdivisions of simplicial homology manifolds. Recently, Kubitzke and Nevo proved that the g-vector of the barycentric subdivision of a Cohen–Macaulay simplicial complex is an M -vector, which in particular proves the g-conjecture for barycentric subdivisions of simplicial homology spheres. In this paper, we prove an analogue of this result for Buchsbaum sim...

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...

Wachspress and mean value coordinates are two generalizations of triangular barycentric coordinates to convex polygons and have recently been used to construct mappings between polygons, with application to curve deformation and image warping. We show that Wachspress mappings between convex polygons are always injective but that mean value mappings can fail to be so in extreme cases.

We present an algebraic account of the Wasserstein distances Wp on complete metric spaces. This is part of a program of a quantitative algebraic theory of effects in programming languages. In particular, we give axioms, parametric in p, for algebras over metric spaces equipped with probabilistic choice operations. The axioms say that the operations form a barycentric algebra and that the metric...

Well-conditioned, stable and infinitely smooth interpolation in arbitrary nodes is by no means a trivial task, even in the univariate setting considered here; already the most important case, equispaced points, is not obvious. Certain approaches have nevertheless experienced significant developments in the last decades. In this paper we review one of them, linear barycentric rational interpolat...