Even the most superficial glance at the vast majority of crossing-minimal geometric drawings of Kn reveals two hard-to-miss features. First, all such drawings appear to be 3-fold symmetric (or simply 3-symmetric) . And second, they all are 3-decomposable, that is, there is a triangle T enclosing the drawing, and a balanced partition A,B,C of the underlying set of points P , such that the orthog...

We study Hoeffding decomposable exchangeable sequences with values in a finite set D = {d1, . . . , dK}. We provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, for every K ≥ 3, there exists a class of neither Pólya nor i.i.d. D-valued exchangeable sequences that are Hoeffding decomposable.

Given a tournament T, module of T is subset X V(T) such that for x,y?X and v?V(T)?X, (x,v)?A(T) if only (y,v)?A(T). The trivial modules are 0?, {u} (u?V(T)) V(T). indecomposable all its trivial; otherwise it decomposable. decomposability index denoted by ?(T), the smallest number arcs must be reversed to make indecomposable. first author conjectured n?5, we have ?(n)=n+14, where ?(n) maximum ?(...

This paper is devoted to the study of higher secant varieties of varieties of completely decomposable forms. The main goal is to develop methods to inductively verify the non-defectivity of such secant varieties. As an application of these methods, we will establish the existence of large families of non-defective secant varieties of “small” varieties of completely decomposable forms.

Balister [Combin. Probab. Comput. 12 (2003), 1–15] gave a necessary and sufficient condition for a complete multigraph Kn to be arbitrarily decomposable into closed trails of prescribed lengths. In this article we solve the corresponding problem showing that the multigraphs Kn are arbitrarily decomposable into open trails.

We give a classification of the triples (g, g′, q) such that Zuckerman’s derived functor (g,K)-module Aq(λ) for a θ-stable parabolic subalgebra q is discretely decomposable with respect to a reductive symmetric pair (g, g′). The proof is based on the criterion for discretely decomposable restrictions by the first author and on Berger’s classification of reductive symmetric pairs.

We study consistency of learning algorithms for a multi-class performance metric that is anon-decomposable function of the confusion matrix of a classifier and cannot be expressed asa sum of losses on individual data points; examples of such performance metrics include themicro and macro F-measure used widely in information retrieval and the multi-class G-meanmetric popular in c...

The notion of sequential and parallel decomposition of a language over a set of languages was introduced by Schnoebelen. A language is decomposable if it belongs to a finite set of languages S such that each member of S admits a sequential and parallel decomposition over S. We disprove a conjecture of Schnoebelen concerning decomposable languages and establish some new properties of these langu...

A tree T is arbitrarily vertex decomposable if for any sequence of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by . An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here. © 2007 Elsevier B.V. All rights reserved.

A class of n-ary Poisson structures of constant rank is indicated. Then, one proves that the ternary Poisson brackets are exactly those which are defined by a decomposable 3-vector field. The key point is the proof of a lemma which tells that an n-vector (n ≥ 3) is decomposable iff all its contractions with up to n− 2 covectors are decomposable. In the last years, several authors have studied g...